ok it's tomorrow.
So,
as other wise men have said, the best thing you can do when you come to europe is to go slow. Think, if you go to a spa, you're already done - you are inside the spa. You just casually use the various services as they come or as they catch your fancy - because you are there to relax. Your destinations may have one or two things you really really must see, but i would suggest limiting these to one every other day at most. You need to consider that our transport is pretty much shit, because some of it has grown out of literally medieval equivalents, and our cities can be quite packed (specially the places where YOU want to go) so "uh i'll just go see THING" isn't gonna be so relaxing and/or straightforward as you imagine.
heathrow is horrible, expensive and slow to get in and out of. the "tube" (the subway) is also long and slow and smelly. As a (former) londoner, i really don't know what the hell you want to see here. Buckingham palace is going to look like shit compared to the architecture you see in Rome or Paris.
London is also wet and dirty and full of fucking people, and really not a great sightseeing experience. I mean, some of the "sights" are allright, but
walking around to see the sightseeing things is fucking annoying as hell.
Oxford is quite charmin, though i have not been in 20 years, so thing may have changed quite a bit. Getting there also is not terribly easy, and i would suggest a day excursion arranged by a company - i know it sounds tacky AF but it's probably easier to let someone else do the legwork to give you a nice experience.
Venice is fantastic. It's fantastic because it's designed to look fantastic, which comes with an extra charge. Prepare to pay some pretty steep prices for everything, but, compared to say Miami Beach, it's reasonable. Also, this is one of those places where having zero plan and just going where your feet take you is by far the best idea. Try to get lost. Explore.
Forget about taking the train. There is a fantastic Eurtostar service from london Paddington into Paris, and then from Paris all the way down to Lyon, but how the fuck are you planning to pass the alps? You would instead need to go to Geneva, and from there in the tunnel, which is like 4 hours underground, out of a 16 hour journey. If you are still planning to do this i would STONGLY recommend that you pay for first class tickets, because european trains can get really, really full, and the further south you go the worse the experience.
There will be big differences in your trip depending when you are travelling. London in Dec / Jan / Feb is to be avoided at all costs. You will be soaked, your shoes will be black with city mud (that's a lovely combination of car fumes and pigeon shit we're talking about here), and people will be constantly bumping into you everywhere.
Traffic in london sucks balls.
Buses suck balls. the Tube sucks balls.
If you delay your trip to Venice until february, you could catch the Carnival. This is an absolutely epic experience that humiliates similar events like the carnival in Rio, but be warned that accommodation will triple in price and the whole fucking city is booked out months in advance.
Italy has fairly decent weather but, i still wouldn't pick the early months of the year for anything except the venice carnival.
Rome is as always a great tourist destination, maybe not as much as it may have been 20-30 years ago (same goes for Paris), but it's still ok, provided that you go march to early-july at most, or september to mid-october.
Edinburgh is lovely and VERY easy to travel. If you are looking for that old-world charm with a Bri'ish tint, then my recommendation is to go to Edinbrah. We say Hed-in-bra, we dont say eydenBURG. Even at christmas (which is fantastic in 'Ed, if a little cold) it's great to visit. The castle has daily tours, there are some fantastic high-end whisky (no "e") tasting bars, you can buy a kilt, the hotels have reasonable prices, and either Glasgow Paisley (GLA) or Edinburgh (EDI) airports have long-haul direct flights to the US.
If you feel adventurous, you can rent a car and just take a drive along the highlands. It's not risky, you don't need to know much aside from keeping your wheels on the tarmac, and it's fairly cheap for the sights. There's also day-excursions to the islands, but it's not a great activity for the winter months.
The EAST side of scotland has a much drier climate (well, so to speak) than the west.
Inverness is also another option, look at some photos online. But, i would go Edinburgh.
I would also offer an alternative to Rome, which is Palermo (direct flights from anywhere). At one point Italy did not exist as a country and there was a thing called the Kingdom of the Two Sicilies; Palermo was the capital, and as such it has incredible architecture, not quite as ancient as Rome, but really beautiful. The food is gorgeous, possibly even better than in Rome, and the weather in Sicily is extremely mild. I would rate it as a low-risk holiday, just don't be a 'tard i.e don't hang your camera around your neck, don't wear shades and a star-spangled shirt, don't flash your wad sort-of-things and you'll be fine.
See, in Europe, if you know where to look, everywhere is nice. But there's places where even if you *don't* know where to look, everywhere is nice.
There's also places where it's very nice on this side, and horrible in the other. I promise you that both Paris and Rome and also London etc have some fucking disgusting places, but so do all big cities.
Now, you could go "remote", villages in Tuscany, in León, in Burgundy, but it's not easy to plan a holiday there, and then be able to actualy DO STUFF.
I also wouldn't know Lisbon, or
Porto, or maybe Madrid, but if you go to Barcelona well, it's a big city where people are busy. Better than London, but again the same kind of stuff. Think of a european tourist looking lost in Manhattan. Do you want to be that guy?
Dublin's quite nice, but the main attraction is drinking.
Amsterdam's quite nice, but the main attraction is smoking weed.
Belgium is .. exists. It is nice, but also extremely
Belgian uneventful.
Geneva is lovely, and so are most cities in Germany. all the central european republics - germany, switzerland, austria are so clean, secure, well organized, that you can just show up without a plan and everything will work out well. These are places where
you go to the police and they help you, instead of beating you up.
They are also not particularly .. "special". I spent a day in Frankfurth and it was all of the above, lovely, but also .. kind of bland.
Paris is beautiful, but if you travel to another french town, you may lose a bit on the beauty, but will be further away from the homeless guys in the streets and the roving bands of
drunk algerinians. And really you can have your pick, Toulouse, Poitiers, Lyon, Marseille (where they do the bouillabasse), but honestly i would go to the riviera - Cannes, Nice, Monaco.
The same goes for Italy. Sure yeah Rome, Milano, but if you go to say, Verona,
Torino (mostly good for shopping), Padova, Arezzo, they all have their charms, and while they might be less "prepared" to host foreigners (i.e. less people speak english) they are also far less crowded, far easier to walk around in, cheaper, and you'll probably find the food more refined.
I would strongly advise you to avoid Naples, and in general the south of italy. it's good for me, but not for you.
Sicily is another matter alltogether. Yes there is a lot of crime, but it's italians on other italians, they don't target foreigners (unless you
move there, then you're fair game).