If you do fancy a boat trip the visit to Halki is also good.
Beaches wise they'll be pretty quiet in mid/late september,the east coast being the best(west coast is pebbles and constantly windy),the main beach at Pefkos is really nice,especially at the end by the taverna with the aeroplane(they do flights out over the bay/lindos at low level,scary stuff!),also worth seeing are the big beach at Tsambika and also Agathi beach which is near the Haraki junction on the main Lindos-Rhodes highway,it's signposted 'Agathi-Golden Sand' and is EXCELLENT for the kids as the water is really shallow for a good 1-200 yards out,with no pebbles or stones and virtually no waves. If you want a quieter beach try Plimmiri,that's pretty secluded and seldom visited by many but easily reached by direct road so no idea really what the other poster means by saying you need to go off-road,there is a proper 'deserted' beach after Plimmiri that is reached in a car by crossing a nature reserve but ideally you'd need a jeep as it's pretty rough ground,but this beach can also be reached on foot as it's the other side of the headland from Plimmiri and has tracks as there's a couple of houses that use them for access. Prasonisi is well worth a trip if you want a huge beach,google the name for some images,the beach is basically a causeway over to a small island and forms a bit of a barrier between the med and the aegean,there's kite/windsurfing competitions a lot of the time down there and also in September if you drive down there you'll see the Greek Army performing an exercise with tanks and artillery on the ranges that flank the main road! Other beaches of note are St Pauls at Lindos and the main beaches of Faliraki,especially if you want watersports and plenty of other activities.
Historic sights include the aforementioned ancient Kameiros and Rhodes old town, there's also the Rhodes acropolis,ancient stadium,ampitheatre and running track up on Monte Smith which overlooks the west coast with views to Symi and Turkey,doable at the same time would be the cross at Filerimos and also Ialysos. Lindos is the obvious choice for ancient sites but it warrants an entire page of it's own,september is also a good time to be there as it's not too hot for the climb up to the top.
Other sites worth seeing would be the butterfly valley at Petaloudes,the natural streams and springs at Efta Piges(7 springs)near Kolymbia,the wineries and vineyards in and around Embona,which is the island's highest up village on the slopes of mount Attaviros and is an excellent place to stop for lunch on any day tour,the mountain roads in that area are a site in themselves,especially beyond Siana towards Monolithos where views across the Aegean to a small group of other islands and beyond to Halki make a breathtaking photo-opportunity.
I've waffled on enough now but there's loads more to see and do for all ages,including waterpark and good shopping etc etc etc
