Ft. Worth is full of museums and cultural events. Fort Worth is one of the greatest cities in the SW for art museums and most are free. Go see a painting or photography exhibit and then head out for some jazz off of Camp Bowie for the night.
The FW Stock & Rodeo show are going on right now.
FW is home of many great theater/play houses. You can find everything from funny campus plays at TCU, TCC, or TWU, children's theater, classic plays at Casa or Stage West, or ever plays at the African America theater called Jubilee.
If you like Italian, FW has some great spots - Sardine's (they also have live jazz) or the Italian Inn - piano music and romantic "private" booths.
If you like Country & Western music, head to north side drive for places like Billy Bob's or out to west FW for the Horseman or Woody's.
FW also has great outdoor things like the botanical gardens, parks, the Japanese gardens, the zoo, and their is also a nature center out west of town (off of Hwy 199, I believe) that is great for hiking and nature observation.
Lake Worth used to have a "riverboat" you could ride on and have dinner & dancing. I don't know if they still have it or not.
There is a romantic French restaurant behind Camp Bowie & 7th street called Saint Emillion's.
You can also see a planetarium show or IMAX movieat the FW Science/History museum. There is also a planetarium up at N. Texas Univ. in Denton.
If you like to shop for antiques and stay in a Bed and Breakfast, take a short trip SW to Granbury, TX. And don't forget Arlington for amusement fun at Six Flags, Wet and Wild, and a few comedy clubs (there might still be a comedy club in Sundance Square, downtown FW, too).
Sundance Square is also a great and safe place to go shopping, site seeing, and get a few inexpenisive or unusual beers. Don't forget to check out the beautiful Bass performance Hall while you're downtown.
Joe T. Garcia's on the north side is famous for it's Mexican food. Cattleman's is also famous for it's steaks. There is a restaurant called Spiral's if you like you like vegetarian food. Also, Reatta and Lucille's have good food.
And the best advice I can give you is to check out the Ft Worth Star Telegram, on Friday's I believe, for their weekly entertainment guide. It will list the majority of the events in and around D/FW for that weekend and upcoming weekends.