For a gentle starter you could take a five mile spin around the Alster Lake near the city centre, shared with joggers and walkers who usually keep to their own side of the path.
For a round trip you might consider a trip on the cycle friendly ferry from Landungsbrucken to Finkenwerder to access the west side of the river. Depending on your wishes/time you could cycle down the west side of the river to Wischhafen where the ferry takes you back across the river to Gluckstadt, then cycle back towards Hamburg along the east side of the river.
Well I managed 4 days in the most glorious sunny weather and summer temperatures. I started with the Alster trip, did some cycling in the Alten Land, the south side of the river, the north side of the river and the Sachsenwald.