It is easiest to do this in very late May or early June - since Tioga Pass may be open by then.....That is a factor and if the snow continues to fall like it has so far this season, it could be a late opening for Tioga Pass (i.e. June....) But who knows - we could get very warm weather again by January and then it might open early.
Since you are in your early stages, I would do it later then earlier if at all possible.
For Mono Lake, stay in June Lake Loop - I would suggest staying at Gull Lake Lodge ...easy walk to two lakes; reasonably priced; and my sister who has allergy problems seems to do ok staying here. its a no frills type place with a small kitchen - but with the separate living room and bedroom makes for a nice place for staying.
From Sacramento I would probably drive Highway 50 to South lake Tahoe and continue to highway 395 (if you want to see part of Lake Tahoe). Drive south on highway 395 to Mono Lake/Lee Vining/June Lake Loop.
I would probably spend 2 nights in this area to see other sites in this area - Mammoth Lakes, Mono Lakes, June Lake Loop;
For Yosemite, the best is to get in park lodging. Check the National Park site for lodging options - I would probably pick the Lodge at the falls...
(Note; Getting lodging will be hard - many book a year in advance).
For Yosemite - I would suggest 2 nights in the Valley - but reservations can often dictate how long you can stay there.
If Tioga Pass is open drive over Tioga Pass - if not its a long day backtracking back to highway 49 and entering Yosemite via the west entrances.
After seeing Yosemite, I would drive the road to Wawona, see the Big Tree area of the park, and plan to stay in Oakhurst. Its a short drive the next day then to Sequoia National park. The Best Western there is nice to stay at with lovely mural of Yosemite painted on the walls of the hotel rooms.
From there go to Sequoia - due to snow, Kings Canyon may or may not be an option. I would stay 2 nights in this area...