Agree about Bally's being an ideal choice. Mid Strip. Plus, Bally's shares an inside walkway with Paris, easy to walk between casinos. Both are iconic properties, lots of food options. Try Mon Ami Gabi (at Paris) for breakfast. Try for a patio table, or atrium (almost on the patio, just as good). We always (every trip, no matter where we are staying) split an order of Blueberry French Toast and an order of their wonderful bacon...big pieces. Comes with all the whipped cream you want. Yikes, I'm salivating now!
Being young as you are, you can enjoy walking the Strip and seeing (inside/outside) the many other Strip properties. (Morning is best for this...milder temp, sidewalks less crowded.)
Not sure what kind of "fun" you are looking for. You will be amazed how fast time flies, won't do all you think you will see and do. Don't plan on making your fortune. Casino Royale may still have some cheaper table limits, if you play tables. Whatever you play (slots, tables, etc.), do short sessions here and there, just enjoy the Vegas experience.
If you are filthy rich you may want to try the nightclub scene, but they expect BIG bucks, like $600 for starters for a booth and one bottle of booze, and fancy dress to even be admitted. Better with a group.
Take some time to visit Downtown. Downtown has its own personality, and has some ideal eateries for a romantic dinner which would not bankrupt you. In the evenings they have the "Experience", a canopy with light shows. Zip lines, other crazy stuff.
SLS is new, but nothing else around it. You might cab down to it to look it over, since it is on your list. But not as your base hotel this first trip (I assume?). Enjoy your trip!
Oh, P.S., every place you eat, mention to the server that this is your birthday. Often they'll present you with a free dessert or something afterwards. That's fun.