I've been going to Eliot Family Practice for years and I really like it there. Dr. Enzinger is great, as are all the nurses I've seen there. I've heard good things about Jennifer Nelson, too, though I've never met her myself - she's also at Eliot and I believe she's a Nurse Practitioner. She used to be at Whole Life Health, and I think she's probably a bit more "natural-minded" than Dr. Enzinger.
The practice is primarily affiliated with Wentworth-Douglass in Dover, but also has access at York. I prefer to go to either of those hospitals over Portsmouth Hospital, even though Portsmouth is much closer for me.
As for after-hours care, if you call you are referred to a nurse triage line at Wentworth-Douglass usually and they will take it from there. They've been very helpful to me several times when I've had urgent issues over the weekend.