nancydrew (love your name!) we never rented a car in 2009, and we're going this summer again, and not planning on getting this time either...if you are staying in the Old Town/Downtown area, you can catch the MTS trolley (public transportation) which can take you to several areas, not
Legoland though...
Here's another option for touring, we loved it, and it's only about $30pp.
http://www.trolleytours.com/san-diego/
It's a hop-on, hop-off tour that takes you to Coronado Island, Old Town, Downtown, Seaport Village, Balboa Park, which is where the zoo is.
By the way, the Holiday Inn Express has a shuttle that will pick you up from the airport or train station, and bring you to the Zoo & Seaworld! They also feature a complimentary breakfast, etc.
http://www.hioldtownhotel.com/services_and_amenities/
We were going to stay there, but decided to stay on Coronado Island instead at the historic Glorietta Bay Inn.
www.gloriettabayinn.com
It's across the street from the famous Hotel Del/Coronado Beach, and we can take a ferry to downtown San Diego or take the Old Town trolley tour again if we choose to!
Have a great visit, we love San Diego, and your kids will love Legoland! The only solution to getting there would be renting a car or you may be able to take the train, not sure where it stops in Carlsbad, if at all, but I'm sure it goes by it because we've taken it from Anaheim to San Diego, and that's what we're doing this summer.