Fort Worth is huge. Just DFW Airport is bigger than the island of Manhattan. What's your budget? Do you have a car? You can't get around very well using public transit. One suggestion is downtown in the Sundance Square area. There's restaurants, bars, Bass Performance Hall, and a movie theater. Another option is the Magnolia area which is a recently revitalized area full of funky bars and restaurants that leans older than West 7th. Another nice area is the TCU area. There's great restaurants in the area as well and the university offers all sorts of cultural programming. You need to make sure the complex you choose doesn't cater to college students though. My final suggestion is the Museum District. There's world class museums in the Fort Worth museum district and their own restaurants plus you're close to the restaurants on West 7th without living there. You're also close to my favorite Fort Worth bookstore, Monkey and Dog.
Each of these neighborhoods has it's own flavor and amenities. All of them are within easy commuting distance of downtown although some are easier than others. If you like to bike or walk, you might also see if the place you're looking at is close to the Trinity Trail network. Biking the trail is very popular in Fort Worth and the trail has restaurants, parks, a food truck park, a Whole Foods, a farmer's market, etc. along it. Recently, my DH biked with our kids on the trail from our home in South Fort Worth to Whole Foods. Fort Worth's mayor is very into biking and likes to have what she calls rolling town halls.
If you want to talk to more Fort Worth natives and learn more about these neighborhoods, I highly recommend checking out the Fort Worth subforum on City-data. You're also welcome to PM me.
