You actually have access to some pretty good places depending if you want to walk or you're willing to get on the light rail.
Samar is a short walk from there and Stephan Pyles isn't much further either. Could also make a lengthy trek to One Arts to hit Tei An, The Commissary, or Screen Door, but it's pretty hot outside so keep that in mind. Tei An would be well worthy of a stop as Teach is the only one doing handmade soba in Texas and one of very few soba specialists in the entire country.
And of course you can get on the light rail via Pearl Station, which is right outside the hotel and opens up some possibilities. You could use any line to go to Union Station and head up to the top of Reunion Tower to do 560. Could take Green Line to Deep Ellum and go to Cane Rosso (my #1 pick if in that area), Local... many options there, just run a search on Deep Ellum.
Consult this thread too for downtown/Deep Ellum in general: