Lake Hodges is a pleasant place to paddle a kayak, although it is closed part of the year. It's open February through October. See website for more information. Each arm of the lake (see GPS routes on triplogs) will give you about 5 miles total out and back. So, if you paddle to the end of each arm you should get around 9 to 10 miles. It is a great place to bird-watch. Motorboats are allowed but cannot go over 35 mph, so it's not as crazy out there as at other lakes. Early morning is best, since afternoon winds can come up.
Put-in for kayaks is at good-sized beach near docks. You can park your car on the beach right next to the water to unload, then move your vehicle further up the beach after unloading.
See link in "Fees / Permits". Tandem is even if paddled by only one person. Fee is sometimes collected by hand, other times you pay the machine. Easy to figure out.
One-half hour before sunrise, to sunset. You can get there early and line up with the fishermen's trucks.
Check out the Official Route and Triplogs.