Neighborhoods on the south end near Hallam, Scott Lake are pretty good areas. Be careful around western Memorial Dr. (Hwy 92).
Hollis Garden is really pretty. Near there is the Texas Cattle Company, a really good steakhouse. Within walking distance into downtown is Harry's, a New Orleans themed restaurant...Palace Pizza is a good casual pizza place. If you go one exit west from where you're staying, you'll hit Lakeland Square Mall with several chain restaurants (Olive Garden, Red Lobster). If you Mapquest Lakeside Village, there are plenty of chain restaurants (Chili's, Macaroni Grill, Mimi's Cafe, Longhorn Steakhouse, Grillsmith) along with a large movie theater and other shopping. Lakeside Village is the newest shopping district in Lakeland; it's south of where you're staying.
Hope this helps!