True, checking out of one hotel into another takes time, but the Renaissance is a beautiful resort and the best when doing DC and SWF. It's located literally across the street from SWF. When you visit DC, you get 7 days at SWF and BGT. There is a free shuttle bus that travels from SWF to BGT and DC.
http://www.nogodforme.com/images2005/SWF073005031.jpg
http://www.nogodforme.com/images2005/SWF073005030.jpg
Since you said you don't want to rent a car, there are shuttles between UO and SWF. The times vary during the year, but for July of last year, it was 10am.
http://www.nogodforme.com/images2005/IOA072905003.jpg
Most people who visit DC like to arrive early, and get an early Dolphin swim. Your swim time is based on when you check in. So if you take the free shuttle from the RPR, you won't arrive DC until 10:30am. That's kinda late. You'd have to take a limo ride from the RPR on your DC visit. You can use the free shuttle for return visits afterwards.
Here's my DC report from 2001 where we stayed at the Renaissance.
http://www.nogodforme.com/SeaWorld1.htm
We stayed on club level and it was awesome.