Howdy Mexican

There are usually a fair few people about on a Sunday, particularly around the city and northern suburbs. Not sure whether there are many group/shop rides etc on Sundays, but you could try ringing a couple of the bike shops - Ken Self Cycles are good guys, as are Ride in Bellerieve and the CBD.
Other than that, I reckon Mt Wellington is a ride everyone should do at least once - but it's no fun unless the weather is good - and the forecast doesn't look fantastic at the moment. Hobart-Margate-Sandfly-Fern Tree-Hobart is a popular circuit of about 50Km - gives you a taste of the views and climbs of Mt Wellington but without getting into the alpine zone

You can throw in a loop of the Tinderbox peninsular by turning left onto Beach Road at Kingston, then rejoining the Channel Highway at Howrah - a three Km stretch of Tinderbox Road is unsealed but rideable on a road bike, provided you're careful and don't mind getting the bike a bit dusty. Nice views of Bruny Island and the coast around Margate, Kettering etc from the southern tip of the peninsular, and terrific views of South Arm and the Tasman Peninsular out to the east. The Channel Highway south of Margate is also good... you can do a complete circuit of the Channel Highway by continuing down through Kettering to Cygnet then up to Huonville, rejoining Huon Road at Lower Longley - which is a great ride but a bit epic because of the length and a couple of biggish climbs as you come out of the Huon Valley then up the Mt Wellington foothills to Fern Tree.
One word of warning in this area though - the Channel Highway between Kingston and Margate, and Sandfly Road between Margate and Longley are home to some of the world's most dangerous drivers... I've rarely ridden there without being elbow-shaved by someone in a white ute or 4WD towing a boat at 100Kmph. It pays to be very aware of what's approaching from behind; I generally move 50cm to the right as they approach, then move left again as they pass; so if they misjudge the 15cm allowance I don't get taken out by their boat trailer.
Another option is to ride up Argyle or Elizabeth St through Hobart, then follow Main Road out to Bridgewater, cross the bridge and ride along Bowen Road to New Norfolk - not much traffic on a Sunday and another scenic ride up the Derwent Valley. Most group rides would tend to be in this area rather than further south IME.
Of course, another option is to string all of the above together for a 200Km+ epic, including climb of Mt Wellington
