I'll give you some suggestions of hotels that are no more than a couple miles off I-65 and within walking distance of casual restaurants (since you are just traveling through):
Downtown - Uptown District
*Sheraton Hotel (Starwood) $150
within one block of
http://www.uptownbham.com/ - TopGolf, Todd English PUB, Texas de Brazil, Cantina Laredo, Eugene's Hot Chicken, The Southern Kitchen & Bar, Octane Coffee, Mugshots Burgers, and Your Pie pizza
Downtown - Parkside/UAB
*Hilton Garden Inn $118
*Courtyard Marriott $140
http://www.railroadpark.org/index.php
http://www.barons.com
Within walking distance of Railroad Park, B'ham Barons Baseball (fireworks on Friday gamedays; one of the best minor league parks in America), Pies & Pints, Momma Goldbergs, Glorybound Gyros, Milo's Hamburgers, Tortuga's Pizza, Good People Brewing Co. (different food truck every evening)
Downtown - 5 Points South/UAB
*Doubletree
*Residence Inn
*Homewood Suites
*Hotel Indigo
(all $115-$200 depending on the night)
http://www.fivepointsbham.com/
Walk to: Insomnia Cookies, Surin West, Jim n Nicks BBQ, Black Market Bar and Grill, Mellow Mushroom Pizza, Little Italy's Pizza, 5 Point Public House & Oyster Bar, J. Clyde, Delta Blues Tamales, Chez Fon Fon, Charlemagne Records, Brennan's Irish Pub, Waffle House, Chick-fil-A, and a few 5-star restaurants I won't name here
Disclaimer: Maybe not the neighborhood to be out late with the kids
This is what I do with my out-of-state family...
Aloft Birmingham - Soho Square $139
Directions from I-65 South:
https://goo.gl/maps/7MnFp5CCVt32 (fastest route)
https://goo.gl/maps/Jzr3pjnsYfz (detour through UAB, scenic overlook, past Vulcan statue)
You've been in the car all day and are ready to stretch your legs. Take a left when you exit the hotel lobby and head down 29th St. Turn left onto 18th St and then right onto Reese St... keep walking until you get to
Little Donkey. Great Tex-Mex and fried chicken. Then get popsicles at
Steel City Pops next door or hit
Red Hills Brewing (also next door). Head back the way you came, but go past 29th to
O'Henry's for coffee/2nd dessert. Before you leave the next morning, walk directly across the street to
Big Bad Breakfast.