Dart Haven has some visitor moorings. All short term and not bookable in advance but they will all be walk ashore plus Dart Haven has good facilities. It's on the Kingswear side of the river but the Lower Ferries get you to the Dartmouth side every 10 mins or so.
Noss on Dart a bit further upriver also has similar visitor moorings. It's quieter up there but you'd have to take the water taxi to get into Dartmouth for a meal, or walk downriver from Noss to the Higher Ferry to get over to Dartmouth.
I'd avoid Dart Harbour authority visitor moorings as they can raft up, meaning you would have a faff if you wanted to depart early for a session and were on the inside of the raft, plus some of their moorings aren't walk-ashore.
Not sure about Paignton/Torbay marinas but I'd guess they are all non-bookable short term too.
If you did go to Dartmouth.... I'd be tempted to take mine down for a couple of nights too.