Either:
Downtown in the River Market, which is only 2-3 miles from the airport. Fewer hotel choices, but lots of local restaurants and pub-style places. Depending on your hotel, maybe within walking distance.
West Little Rock is at the other end of I630, 10-15 minutes depending on traffic. Way more hotels and restaurants, mostly major brands and chains. But you'll need a car to get around.
For a single night, I'd go River Market. You could probably get away with no rental car, there's an inexpensive trolley line that runs through there and downtown North Little Rock, also taxis and Uber. TAC Air will probably drop you off at the hotel and Pick you up when you're ready.