I suggest checking out Lisa Foster's guidebook.
Regarding where to go, you'll be limited by the availability of backcountry permits (opening day to request permits was on March 1st). The west side does not see as many visitors and it is beautiful! However, park wide they are fighting invasive pine beetles, which has killed more than 1/2 of the lodgepole pines (it's quite the site to see). I'm unsure what the snow/trail conditions will be like that time of year since I typically go in the early fall.
If the trails are reasonably clear, I'd suggest considering the east inlet trail. Hike to the Lake Verna campsite on day 1 (start before 7 am). Leave your camp setup at Lake Verna on day 2 and hike to either the Boulder-Grand Pass (involves some off trail steep inclines to the continental divide) or go 5th lake. Return to Lake Verna on night 2. Day 3 would be spent hiking out and exploring as you decend back to the Grand Lake area.
This link shows some photos from my east inlet 3 day hike in 9/07:
You can pay ($5) for a shower at Elk Creek Campground (located at 143 Golf Course Road, Grand Lake, CO, phone 970.628.8502)
In Grand Lake, breakfast was great at the Black Bear Bakery and Cafe. Sagebrush BBQ was a nice relaxed place for dinner. Grand Lake Chocolates has great ice cream. Spirit Lake Lodge was a clean, reasonably priced location to stay the night before the hike (during certain times the do not permit 1 night stays). Be sure to spend some time in Estes Park and drive through the park via Trail Ridge Road.
www.rmnpforums.com has some more focused/local area posters that are knowledgeable.