If you got a day and like mountains then I would suggest.
Savanadurga
Skandagiri
Nandi Hills (Definitely for Sunrise) Or you can spend a day at Muthayala madugu. ( a jungle without wild animals) Bangalore palace There are so many parks to relax/go for a walk in Bangalore but not the ones that you find unique from the regular ones.
According to me you should definitely check out Devarayana Durga hills and basdi hills(Mandara Giri hiils) near Tumkur. They offer a best scenic view in all seasons.