No Hiltons within walking distance of the Hyatt. But the Anatole is 2 miles away (also ES, HGI, DT and Homewood in the same area. And the Park Cities is 5 miles away.
The DT-Campbell Ctr is 5 miles, across the street from NorthPark Mall and near good restaurants. the Embassy Suites at the Galleria is nice, but 11 miles from downtown.