Look in the local Yellow Pages under "Video/Production Services".
Assuming that this is on old 8mm stock and also that the movies were shot/edited by a parent consider leaving them intact, instead of re-editing them.
A few things to think about:
1. Do you want to have the movies re-shot to 8mm film as chances are that the original film stock is not in great shape? It, the original film, may also become further damaged during intitial playback. Our family film required some work (beefing up) just to make the t/f to VHS tape, but it was 25+ years old @ the time.
2. If having a film copy made is of no interest, then consider paying a bit extra to have a few copies made on VHS tape. From what we understand @ this point about DVD/CD disc copies, they are not of archival quality (it would be a shame to lose such family history 10-12 years down the line due to data loss). The add charge for this should not be much.
Though the standard line/joke is "oh no, not home movies" I have found that most get a kick out of watching ours (they were shot in the early to mid 60's). Think that they will make great gifts.
Not certain about varying quality between service centers. I used a pro/commercial service that did some minor touchup work gratis (the manager is an old friend), but don't expect your copies to be better than the originals, based on the film's condition, unless you are willing to pay for such services (which are not inexpensive).
I did not really want ours cleaned up anyway as I recall seeing imperfections (fireflies, dust lines, tons of editing splices, etc.) on the originals as a child.