You do often get quite different weather in Riva to that in Sirmione due to Riva's close proximity to the mountains. Last year the majority of April was lovely in the area but often it can be quite wet. Weather wise is usually very mild in April/May but as anywhere you can't be sure of what it will be like. It can at times be a bit windy though that is more confined to Torbole where ythere is a lot of windsurfing.. I personally would go in early to mid.May to take advantage of the warmer evenings for sitting outside at the numerous restaurants and cafes. Riva is a really nice old town and there is a lovely walk along the lake side towards Torbole or walks of a more taxing nature up in the hills behind the resort.
You can take the usual hydrofoils and ferries to other places on the lake, Malcesine and Limone come to mind. Riva is really attractive holiday destination and not as overcrowded with day tourists as Sirmione tends to be.
I'm a semi frequent visitor to Lake Garda and have stayed in quite a few towns on the lake side, I tend to head for Bardolino or Garda Town as I like the long lakeside walk between the two towns and wandering round their small alleyways . I have stayed in both Malcesine and Limone both are rather hilly towns. The northern resorts though have the most attractive scenery.

Thanks, Judith, it will be a 60th birthday present to myself, so May will probably be better (closer), although more expensive.
Good info. I have only got as far as Garda village, beautiful.