I went to Tonga last September and loved it. Didn't do any climbing but did try (admittedly half-heartedly).
We stayed mostly in Ha'apai and Vava'u and unfortunately didn't see 'Eua.
Ha'apai is made up of coral islands (flat) except Tofua and Kao which are volcanoes and very hard to reach without your own boat. I highly recommend staying a few nights on Uoleva if you're looking for idyllic South Pacific remoteness on an almost deserted island. If you go swimming with the humpbacks, do it in Ha'apai and avoid the relative circus of Vava'u.
Vava'u is comparatively not flat. The rock in Vava'u is predominantly extremely sharp limestone (presumably very young with minimal weathering to the point that limestone is probably a misnomer). We rented kayaks and tried to find some DWS spots (even brought our shoes and chalkbags) on and around Otea island but the rock was just too sharp... basically like climbing on coral fragments.
Tongatapu probably doesn't have any climbing (and is best avoided anyway). The Niuas (far north remote islands), who knows?!
So I'd say your best bet is trad climbing on 'Eua. It would definitely be on the adventurous end of the climbing spectrum. The only info I could find was a few posts around the web from that former US Peace Corps volunteer.