I have been living in Saipan for about 9 months. Saipan has the Grotto... really a one of a kind dive. It is a fair climb down the stairs to it and back. I have diving friends here who have dived The Grotto literally hundreds of times and never gotten bored as there are so many facets to it passages, walls and caves. There are several good dive operations. I personally go with Eric Javier from Speedy Tertel (sic). he is a professional photographer, and is teaching me how to use my camera. I'm assuming here English is your preferred language. If (as your name suggests) it is Russian, then Sergei at Speedy Tertel is your man. Ex-SPEZNAZ, very skilled, long experience. Harry Blalock at Axe Murderer tours is also good, and friends have dived with other shops with good results.
Aside from The Grotto, there are a number of very good shore dive spots. The Tinian dives are mostly conducted as boat dives from Saipan, as Tinian is only about 4 miles south of Saipan, and the main town on Tinian is on the other side of that island from the dive sites. Be aware that even if you sign up for a Tinian dive, on the day of the dive the boat may change its mind and not go there at all. The sea conditions at the Tinian sites seem to be less predictable than those around Saipan for some reason. I'm told that many Japanese dive groups don't like even mildly rough water, and if it is just one or two of you on the boat and the rest from another dive party that is not up for slightly rough water, you lose. If you want to see the atom bomb site, North field, and Runway Able, then fly to Tinian and rent a car. It is a very short flight in a light aircraft.
There will be more than enough to do, as there are really amazing things to see above the water as well. The Flame trees will be out by then, and the island is spectacular. Any one of the resorts will be quite luxurious enough. As with what I have encountered elsewhere in the area, the resorts cater to the Asian market, but I don't find that objectionable...just a little unusual. If you just want a comfortable bed and don't need to be right on the water in a resort, then try the Century hotel.
It is a couple of hundred dollars for the flight to Rota. There is no boat service to either Tinian or Rota. I have not heard much about diving there, but it is also said to be quite lovely and quiet. I will be going to look in a couple of weeks myself.
Guam is considered the nearest big city for us, and folks regularly go there to shop. I don't know of anyone here who takes their dive gear when they go there for the weekend. It may be great, but not so much that those who live here make a special point of going.
Having said all that, if I were going half way across the world just to dive, I would probably go back to Palau. But if you are on Saipan for other reasons, you will not be disappointed.