Most travel agents have pre-booked rooms with various owners throughout Naxos and other Islands and sometimes limits what you want and where you want to stay.
It's very easy to book your own trip via the internet. You can book a flight or a ferry, you can contact accommodations owners on your own and probably get a better price and customer service.
I stayed at St. George Beach just a short walk from the waterfront and Naxos Town. There is a good beach and a small town square with shops, markets, and tavernas nearby if you don't want to walk to Naxos Town or for a change of pace.
I think St. George Beach would be your best bet. In addition the bus station to get to a number of villages and areas of the island is just on the far end of Naxos waterfront.
I've never used a travel agent and found it's really easy for a do-it-yourself trip. However, I understand the convenience and less stress of using a travel agent but if you haven't booked as yet just do a bit of research for your trip to Naxos. It will be enjoyable, fun and educational.
You can use the below websites for info on Naxos:
http://www.naxos-island-greece.com/
https://www.naxos.net/
For a lot of choices for St. George Beach go here:
https://www.gtp.gr/AccomodationResults.asp?ID_Loc=11979