Finding a place to stay and dive your first time on Coz can be daunting and most folks end up jumping around a little before landing on their "favorite".
Most dive ops pick up at most hotel/resort/condo docks, there are a few exceptions, of course.
We stay and dive with Blue Angel, for about a dozen years now. Small 22 room, 4 story hotel, with all rooms with private balconies facing the ocean and pool, (except first floor that opens up to ground/pool level patios).
About a mile south of town, fairly easy walk to town, I think, $5 cab ride? not sure we rent a car wen were there. Large rooms, with mini-fridges & safes.
Full service 5-star PADI dive operation and school (Blue Angel Dive and Scuba School.. B.A.D.A.S.S.) Morning, mid-morning, afternoon, twilight and night dives all available. "fast boats" (the 6-pack Panga, can hold up to 8 divers + DM depending on how it is licensed) and larger "cabin cruiser" type boats available for larger crowds (they usually use one of these on the 11am trip, which accommodates cruise shippers and folks coming over from the mainland. If you are thinking about getting more certs, I'd recommend Matt (Mateo) Moran, dive instructor at Blue Angel for that.
A very good restaurant, with free breakfast, (free breakfast may only be on dive days, not sure). Open breakfast, lunch, happy hour and dinner.
Pretty good shore diving around the stingray enclosure next door and out to the South. Coz isn't known for it's shore diving, but there's a lot to be found on this dive.
again, MOST dive ops will pick up at BA, if you are not diving with them and they have no problem with you just staying there and diving with others or mixing it up as you are talking about
Other dive ops I'd recommend, no particular order:
Dive with Martin
Aldora
Tres Pelicanos
Bottom Time Divers
BlueXTSea
we've only stayed at a couple other places, now both AI's and I would recommend NOT doing and AI, as there are way too many great restaurants in town to put yourself through the daily buffet routine.