The most obvious day trip from Jinja is Kampala, 80 kilometres west. The road is decent and the journey takes about two hours each way, making it feasible as a day trip — though most people base themselves in one city or the other rather than commuting between them.
Mabira Forest Reserve, about 15 kilometres west on the Kampala road, makes a half-day excursion for birding and forest walks. It's well set up with marked trails and a resident guide; see the Mabira Forest entry under Things to Do.
The western shore of Lake Victoria is accessible from Jinja for boat trips and fishing communities, but it requires more planning — the shoreline is not well-served by regular transport and you'll likely need a hired vehicle or a tour operator to organise it properly.