Do not ride your bike out to Tybee! Some people do it, but that road is extremely dangerous, particularly this time of year because of high speed traffic and the lack of shoulder. There is sort of a shoulder, but it is covered with road tire puncturing debris and rumblestrips. Perhaps you could do it very very early in the morning, but it still might be a death-defying experience.
There are some good rides closer to where you'll be staying. On Bull Street just north of Liberty Street in downtown Savannah at the Gallery Espresso coffee shop, a big group rolls out at 8am on Saturday. There are different levels for this ride. The more chill group will do about a 30/35 mile loop. It's been a while since I've done it and the routes change from time to time, but the hammerheads tend to do more like 40-50, and it is fast. Sometimes, there is an intermediate group that does the longer distance but closer to a 20mph average. Show up to the coffee shop early, introduce yourself, and ask what's going on that week.
On Sunday, there's a ride from the same place, but I think it leaves at 9am. It tends to be long and fast, but they may add a "B" group if there's enough interest.
Bikes are allowed on the Talmadge Bridge, but it is part of I-16, so ride it at your own risk. The shoulder is not clean, but people do train on it from time to time. It is a major climb.
There's an easy 30mi out-and-back from downtown (near the Civic Center) that starts out Old Louisville Rd. Follow this
map out to the intersection of Pine Barren Rd and GA-17. (the loop goes clockwise, so look at the side opposite the airport for these roads) Then turn around.