Hi,
I just returned from a HHI trip with my almost-5yo and almost 8yo. We were also there two years ago, when DS was just-turned 3. Both times, we had a blast. It helped that the weather was near-perfect both times, highs in the mid-80's with bright sunshine.
If you haven't been to Disney's HHI and are expecting something similar to WDW, you're in for a shock. We go to HHI to just relax, even with small children. The resort is on its own little island and is really secluded. THere is a great pool and a kiddie pool at the resort. THere's also a playground, a shuffleboard court, a pier overlooking the creek, and the rec center where you sign up for activities. When we were there two years ago, we did two of the activities - the dolphin cruise (which DS didn't really enjoy) and the unbirthday party, which he did enjoy. There aren't a lot of sponsored activities for a 3yo. DS just really enjoyed the pool (we got a life jacket from the rec people, which he kept all week), the playground, and the beach (more about that later). If your son rides a trike, bring it along if at all possible. If he has graduated to training wheels, they have small bikes with training wheels to rent. Both times my entire family rented bikes, with a child seat on the back of DH's bike for my son to use for the longer trips (such as the beach house).
Disney also owns a beach house about 1 1/2 miles away, which is a comfortable bike ride unless you're really out of shape. The beach house has a pool (not lifeguarded) and direct access to a beautiful beach. If you're going during the summer, bring some cheap sand toys, rent an umbrella and chairs (they'll rent them right on the beach), and spend at least a few days at the beach. When the tide goes out, there are wonderful pools left behind that get quite warm and are shallow enough to splash around in. IN fact, if DS enjoys toy boats, bring one along for him to create his own private lake.
We haven't ever made it to Savannah or even to the tourist sights on HHI. We spend all of our time at the pool, playground, beach, or on bikes. You won't have a lot of time away from your son, but if you get in the relaxation mode, you'll have a fantastic time.
Enjoy - I'm already wishing I were back there!