For sure man! A charter will probably get you a lot bigger fish but just know: there is fish on literally every beach there. When the tide is high and the waves are crashing right onto the high beach sand bar, you can see the jacks jumping onto the sand trying to smack a fish from time to time, specially during sunrise and sunset. Trust me if you don't bring a rod you will end up renting or buying one anyways.
Try to bring like a 1.5oz GT ice cream, some small 1 to 2oz jigs, some medium/large poppers, some jerk baits, stick baits, and some bucktails -> (Mainly if you are looking for snook). You could also throw a good old swimbait honestly almost anything will get you a bite if you somewhat know what you are doing.
Some beaches you could fish are the north side of sayulita's main beach, the rocks on the south end are also good for snapper. There is another beach called "Malpaso" which you have to walk about 15 mins from where the road ends on the north side of town. There is a very clear trail through the jungle that takes you to this beach. It's mostly empty since it's harder to get there but when conditions are right you can find fish a lot closer to shore.
There many other very good beaches you could try all around the area but you would need a ride or cab to get there.
Don't forget to ask around also, locals and your charter guides could guive you good advice on what is biting right now. There is also a specialized surf fishing shop called "Spectra Mexico" located in Bucerias. Stop there on the way from the airport to sayulita and they will definitely have the best knowledge.
You can catch a lot of things from the surf but most people go for snook, roosterfish, snapper, sierra, jacks, and even dorado at times.
You can cast a popper or jerk bait at the rocks to try to catch some snapper and what ever else might come along. But mostly try to cast past the surf with your favorite lure and hope for the best. You can scout the beach and find the rips and currents where there might be fish. Also try to look for blow ups and foamers, the fish sometimes push the bait all the way up to shore.
Good luck man!