My experience with both spots as far as fishing is concerned is poor.
Elliott Heads is a great place but the sandflies are something to deal with as they are very very friendly.
Woodgate is much better as you can pump Yabbies in Theodolite creek and there is usually plenty of soldier crabs so the kids have a ball just catching bait. The kids can also have a ball at Theodolite creek on the beach side catching on the making tide whiting and flathead all undersize but they don't have to wait long for a bite.
I took a boat to Theodolite creek many many yrs ago but the fishing was poor but off the beach if the weather was calm a few mackerel can be caught. I don't know about boat fishing in the Elliott river.