When are you coming? Weekday or weekend?
I don't usually recommend DFW without a car, but for just a day, you can probably manage. The TRE train runs 6 days a week (not sunday) between downtown Dallas & downtown Ft Worth, with a stop near DFW at the Centreport station on the south side of the airport. There are free shuttles between that station and the terminals.
If you want to try to do both cities, I'd suggest Dallas by day. JFK stuff (JFK memorial, Dealey Plaza, 6th floor museum), then the Arts District (DMA, Nasher). Ft Worth in the evening, the Sundance Square downtown offers lots of bars, restaurants, nightlife. These areas are all walkable from the TRE stops.