Mexico is the obvious answer.
Yeah - from LAX there will be a lot of easy options to Mexico. Haven't been to Los Cabos but I've heard good things. Mexico is a bit tough on United miles as they charge 35,000 RT PP but I would think airfare would be fairly cheap to a number of locations from LAX.
If heading to Cancun I would look at Le Blanc and Secrets Maroma. Secrets on the Vine recently opened and while its in the hotel strip and a bit more squished than Maroma they've been running sales. It is $287 per night for 2 for the dates we are looking to go in November so its a bit cheaper than the other two. Those tend to be a bit more calm than other party locations but there are plenty of those too
Out of curiosity I looked up United award flights to some areas in the Carribean from LAX. They have shit availability to Barbados and St Kitts and marginal to St. Maarten, Turks and Cacios. Some dates here or there but some trips were upwards of 36 hours and that was just getting down there. Jamaica was a bit better but Punta Cana definitely looks the easiest to get to of the ones I looked at
It might be worth some of your time to figure out where you
could go on United miles and then work back from there. Some people don't like doing that as they get so focused on the destination that they don't want to go anywhere else. We approach it as a 'Where could we actually fly?' first and then select interesting locations based on our available flight options
What site did you use to book/research?
I have found Kayak and Costco to be the best two options. There are a ton a different Mexico\Carribean websites you could book through all running various different sales on different places at different times and Kayak will cover most of them. Costco will often have nice bonuses like resort credit and\or costco cash card