Although March is not yet pool and/or swimming weather at the lake, you might try and leave some time open to do the Colorado River float trip.
March, though still a "transitional" time between winter and spring, can sometimes offer some fairly pleasant weather. Sunny but brisk, that kind of thing. Temperatures in Glen Canyon, where the float trip occurs, are typically a few degrees warmer than the rimside. You'd probably still need to dress warmly on the raft, but the scenery is still beautiful. Plus this particular stretch of the river has no rapids at all, so you won't get wet unless someone gets a wild hair and decides to jump in ;-) March is shoulder season, so reservations can usually be obtained on shorter notice. Maybe keep an eye on the weather and if it cooperates, bonus - you get a raft trip. www.raftthecanyon.com or 928-645-9175 The float trip runs once daily at 11 am in March.
As for lodging, everyone has given good suggestions. If you want to splurge a bit, but not go totally overboard, maybe consider the Lake Powell Resort. Great location, extensive complex w/all needs (dining, shopping, etc.) able to be met on-site, short distance from town. In my case, whenever I visit Page (lived there 15+ years, occasionally return there for business, family visits, etc.) I stay at Debbie's Hideaway, which is in one of the residential areas of town. For about the same price as a traditional hotel or motel room, you get an apartment with separate sleeping rooms and a full kitchen. I personally prefer to do my own cooking seeing as though I've made the rounds of all the restaurants in town.