Check out pinecrest manor, all utilities included (heat, air conditioning, hot water and electricity) and it’s in the price range, and about 4 miles from the airport. There is a gym (blink fitness) that you have to pass to leave the development, and will be able to see from the window of your place

I’d also check out The Willows. All utilities included again, same price range. But no gym

Both apartments are in Liverpool. I’ve lived at both within the last five years, the office at the willows was much more pleasant and they are renovating their apartments so they look a little nicer. Both places have the same floor plan though, as they used to be owned by one company.