If you are staying near central Bangalore, you can cover several attractions without making the day too rushed. Cubbon Park is a good starting point for a relaxed walk, followed by nearby museums or historic places. Bangalore Palace and other central attractions can also fit into a sightseeing plan, depending on how much time you have.
For a history-focused day, you could combine a museum with a nearby heritage attraction. For a more relaxed plan, pair a park with a cultural place and finish with a local food stop.
The main tip is to group places by location. Choose two or three major attractions for the day and leave enough time for traffic, meals, and breaks. This gives you more time to enjoy each place instead of spending most of the day travelling between attractions.