Vacuum and wipe walls and ceilings, and dust all surfaces. Pay special attention to switch plates and the outside edges of doors, where people tend to grab.
Let it breathe. A good airing will reduce the allergens and germs in mattresses, even if you can't lug them outside. Follow the advice of the Victorian era's go-to guide, Mrs. Beeton's Book of Household Management: "Throw the bed open, by taking off the clothes; open the windows (except in rainy weather), and leave the room to air." In Mrs. Beeton's day, housemaids left the windows open for a half hour, but if it isn't too cold, a few hours is even better.
Head to the washing machine. Once all the linens—sheets, pillowcases, quilts, duvet covers, mattress pads, dust ruffles, shams—are off the beds, wash them in order of what goes on the bed first (i.e., start with dust ruffles and mattress pads; end with shams) so you can put them back on the beds as they come out of the dryer and not have to worry about them sitting in a heap and getting wrinkled. If you're switching over to lighter quilts, wash the winter bedding before putting it away, because moths and other insects are attracted to body oil, perspiration and perfume.
Clean window treatments. For heavy drapes, use the upholstery attachment on your vacuum, or have them dry-cleaned; light drapes can go in the dryer on the fluff cycle with a dryer sheet.
Wash mirrors and the insides of windows.
Shampoo or steam-clean wall-to-wall carpets and area rugs. Some manufacturers will void the warranty if you can't prove that you've had your carpets professionally cleaned every year. Either buy a professional-grade carpet cleaner (which costs around $400) or rent one (many supermarkets now offer this service).
Next: The kitchen (and how to get stubborn grease off of stove grates)