I'd agree with Kolor-Pikker to not look to a "cheap" printer for good quality photo printing. Some folks have gotten inexpensive "all-in-one" printers and have said that they are happy with the output, but still the saying "you get what you pay for" does apply, and like Kolor-Pikker mentions, you pay a lot for photo-quality ink and paper.
Another reason for looking at an outside print service is that you can get prints that are larger than your basic 8.5x11 paper. For hanging prints on a wall, I'd call that important -- the prints I hang are larger, typically 12x16 or 12x18, both of which require a larger (more expensive) printer.
I've used "cheap" printers plenty when I need "office" documents, that's about it. They are great for that when you need paperwork!
As to a local print provider, the one "chain" store that has the best quality if you are in the US is Costco. Sure you can get a "nice" print from Walgreens, or you can be disappointed. Walgreens is "brainless" when it comes to prints, but Costco has a reputation of having good quality print staffers.