A practical one-day plan could start with Lalbagh Botanical Garden in the morning. It is a good place to begin because you can explore the gardens before the day gets too busy.
After Lalbagh, head towards Tipu Sultan’s Summer Palace and Bangalore Fort. Both give you a glimpse into Bangalore’s history and can fit well into the same part of the itinerary.
From there, continue towards Cubbon Park and Vidhana Soudha. These are close enough to combine with the central Bangalore sightseeing route. If you have time, you can also visit Bangalore Palace later in the day.
For the evening, I would suggest Church Street or MG Road. You can walk around, have dinner, and experience a different side of Bangalore after visiting the historical attractions.
A simple route
Lalbagh → Tipu Sultan’s Summer Palace → Bangalore Fort → Vidhana Soudha → Cubbon Park → Bangalore Palace → Church Street
I would not try to add attractions from far outside the city on the same day. Bangalore traffic can make even short distances take longer than expected.
If you have only one day, the goal should be to experience a mix of gardens, history, architecture and local city life, rather than checking off as many attractions as possible. Leaving some buffer time between places will make the day much more comfortable.