Definitely do something tropical! You could fit a lot of fun activities into for a weekend trip & there will likely be a lot to do close to where you're staying (great restaurants, shopping, beach time, snorkeling, jet skis, dancing, etc.)
Miami, DR, Jamaica, & PR are all good affordable weekend trip options.
Check the travel sections of Groupon & Living Social! They always have good weekend getaway deals. Some of them are even all inclusive.
If the beach is not your thing, then maybe a touristy trip to a big city is an option. I'm not sure where you are but places like NYC, Washington DC, Chicago, & San Francisco are good tourist cities.
However, if you're going to a big city for only a weekend, I suggest you do TONS of research before hand. Otherwise you'll spend most of your time getting lost, figuring out where everything is, and finding affordable fun things to do. You don't have time to waste for just a weekend trip, so it's smart to have an entire itinerary (that includes directions & transportation options) laid out for big city trips.
Personally, I think the beach is a more relaxing option.
My first trip with my ex was to meet his family
Don't get me wrong, I LOVED his family & I still do... But a romantic getaway would have been better for a FIRST trip lol.
Have a good time!!