Dallas and Fort Worth often get clumped together into "The Metroplex" or "DFW". While they are extremely close and their suburbs run together, I think they're best explored as two distinct cities. Each has a unique feel and enough to keep you busy, so there's really no need to bounce back and forth. If you want to see both cities, we recommend spending some time in one and then moving on to the other.
Dallas Museum of Art
Check the website for the latest information, but this large museum was completely free when we visited. There were some traveling exhibits that you could pay for. Personally, I thougt the free areas of the musuem housed more than enough art for a visit and the traveling sections were kind of small. I'd recommend only paying if you're really interested in that particular exhibit. The main houses a vast collection, including pieces from many notable artists.
THIS is where President Kennedy was shot. There ARE a few informational panels around to help you understand more of what happened. A few blocks away is a memorial built to President Kennedy.
The George W. Bush Presidential Library & Museum
We recommend seeing this as it's a great history of both the Bush presidency and political affairs of the 2000s. The museum is interactive and very well put together
We always enjoy walking through a downtown area. As with anywhere, best to do this during the day. Some neat buildings and architecture. Plus, where else can you see a giant eyeball?