lwilliam-There are three hotels at Disneyland that are Disney hotels...the Grand Californian (which gives you direct access to California Adventure right from the hotel lobby...the hotel looks a lot like Ft. Wilderness, designed by the same guy), Paradise Pier and the Disneyland Hotel. The Dland hotel is the original, of course it's been remodeled and Paradise Pier was hotel that Disney took over and remodeled. The Grand Californian is fairly new and is very Grand, that's for sure. They all have walking access to Dland, California Adventure and Downtown Disney, with the Grand Californian being the closest (it's located in Downtown Disney). The entire Disney complex is small and compact, you'll be able to access everything by foot and fairly quickly (do you get how small it all is?). It's all very pretty and well organized, as you'd expect from Disney.
Getting to Universal may be a challenge without a car. Anaheim, where DL is, is at least 45 minutes by car (longer if there's traffic, which is very common in CA) from where Universal is, which is in Los Angeles. There may be a shuttle bus, not sure perhaps Disney (dare I say) can help you with that. I'm originally from NY and the one thing I know about CA is it seems you basically need a car to go anywhere. Public transportation sucks to be blunt.
Two (maybe three days) would be enough at Disney. There are the Disneyland and California Adventure parks to see there and Downtown Disney has a ton of restaurants, etc. Universal would not require more than a day. That would be enough time. You'll have fun!!!
Lisa