Oakleigh (from Pelion) is one of my favourites - quite spectacular looking down on the spires, and out to most of the OT mountains. I think the mud puts some people off, but it's pretty dry at the moment (at least it was this week at the Walls of Jerusalem). And while i did put my foot into an 'untapped' spot (hadn't tested it with my pole), and went in up to my waist

, it wasn't the thick boot-sucking mud of the SW - much easier to get out of.
Haven't been there yet, but places like Paddy's Nut, Achilles etc sound great - check out this site for photos & track / route info. I guess it depends on the ages / fitness / experience & comfort with rock scrambling & off track routes of the party. (I think i'd need help negotiating some of those bits, being short & not good with heights

) I reckon make sure the kids enjoy it, rather than taking on something that might be too hard. What would be the hardest Tassie walks the family has done?
Oh, and often when Ossa is clagged in, Pelion East is ok, and is well worth a climb. Though the summit tower can be a problem when it's icy - no grip to pull yourself up with. Even so, the view from part way up the tower is still fantastic. (It took me 6 goes to get to climb Ossa without ice / sleet / snow, and I still have to go back for the summit view.)