For a real mining and historic experience be sure to spend a day and an evening at Sovereign Hill. Also visit the Eureka Stockade exhibition, the botanic Gardens and the wildlife park.
I agree--there's more to see and do in Ballarat and BigW has listed some of the best things to see there.
A third vote for Ballarat and the attractions listed by BigW.
It also has a number of good places to eat and stay and if you are after a mining town you can't do much better than where the Eureka Stockade occurred.
I love both Bendigo & Ballarat but if I needed to choose one I'd go to Ballarat.
Ballarat is physically closer by about an hour and has a specific place to visit and spend the day at - sovereign hill. Not a cheap visit, but you will definitely get a good idea of an old mining town.
As to your question re the rhododendron gardens, the peak blooming season will be over but there will still be plenty of rhododendrons in flower. It's a stunning garden at any time and worth a visit. If you don't like to walk take the little train. It's a very steep garden.
Bendigo has different attractions.
You can go up the old minehead at Central Deborah mine, then take the historic tram via the centre of Bendigo ending at the Chinese Joss house and musuem.
I have been visiting these cities regularly since the early 1960's and love them both; for different reasons.
The attractions of Ballarat have already been mentioned.
Bendigo is different. There is the magnificent victorian era streetscape along Pall Mall. Then the huge cast iron fountain at Charing Cross. You can visit the goldmine at Central Deborah which is in the near southern suburbs. The catholic cathedral is a magnificent sight. I always remember my stay at the Shamrock Hotel and hope to stay there again on my next visit. Then of course there is the Joss House at North Bendigo. Bendigo has a rich chinese history which these days is centred on Bridge street. Particularly when there are festivals, of any kind, they bring out BOTH of their ceremonial dragons. Easter Monday is a particular case.
It is not either/or with Ballarat & Bendigo, you shoudl endeavour to visit both.
I second Les' post. Both Bendigo and Ballarat are truly beautiful places to visit. Do try to visit both if you can.
Ballarat. It is a picturesque area with interesting and quaint shops. Sovereign Hill is really a living museum.