If you're in the US, there are a number of commercial mail-order outfits that do B&W work. One I've used once or twice, before getting the stuff needed for doing my own B&W, is ABC Photo Lab in Connecticut. I was satisfied with the results I got at the time, but as others have said, doing it yourself will give you better control and is ultimately the way to go.

One possible issue with commercial photofinishers is that they sometimes use color paper even for B&W prints. It can be tricky to get a good neutral gray from these papers, so you may end up with B&W prints with a slight (or not-so-slight) color cast. This will also happen if you develop a roll yourself and then take the negative strip to a 1-hour lab to get prints. Note that this comment applies to both conventional B&W films and C-41 B&W films.

As to C-41 B&W films, Ilford XP2 Super has already been mentioned. Kodak has another one, which usually goes by the name BW400CN, although that name is not prominent on the box. BW400CN is available in some local drug stores in my area (Rhode Island), but the Ilford is harder to find locally. Both are good films (although neither pleases everybody), but they differ in one very important respect: XP2 Super has a nearly clear base color, which means it prints well on conventional B&W paper. BW400CN, by contrast, has an orange base color, similar to that on most color print films. This makes the BW400CN easier to print on color paper but harder to print on B&W paper. A digital minilab can likely handle both films tolerably well, but some labs will bungle the XP2 Super and produce prints with ugly color casts. OTOH, some labs (but not most minilabs) will print XP2 Super on B&W paper. Thus, which of these films is better if you don't have your own darkroom depends on the lab you're using. If in doubt, ask the manager of the lab you plan to use. FWIW, my local Walgreens, which uses a Fuji Frontier, produces decent results from both film types; even side-by-side with a print on true B&W paper, the color cast is not objectionable, at least not IMHO. (Others might look at the same prints and disagree, of course.)