Naxos is very windy in summer so for sure you will have enough wind, bring the small kite (like tarifa, which I believe is your usual spot according to your profile). Mikri Vigla is the beach where the kiting is happening (several kite schools there). To get to Naxos, you can either take the plane or ferry directly from Athens or (as you mentioned) from any of the other islands (ferry from Mykonos will take around 90min). July is the peak season but surely you will find some cheap place to stay around Mikri Vigla, there are many options.
We stayed https://www.airbnb.ca/rooms/9444709?loc ... 1&adults=1
, its about 70m from the kite spot.
Rent a scooter to get around to Naxos town (8km fro Mikri vigla).
Mykonos is way more commercial than Naxos, due to its airport. (The airport in Naxos is tiny, so only small planes can land there, which markedly reduces the number and type of tourists compared to other islands such as Mykonos or Santorini). Not sure about the kiting in Mykonos, but there are spots for sure.
The good thing about Naxos is that there are many other things to do if you do not feel like kiting, Paros is also not far so you have some alternative spots close by.
Nightlife in Naxos is probably not at the level of Mykonos and Santorini but I am sure you will find some spots for it.
Naxos is definitely worth a visit, the water is crystal clear, the wind consistent and the food amazing!