Hi Chandhana,
As Kamala suggested , Basil is good though i feel Swathi might be too crowded. Frankly, i hv heard that the traffic + crowd has turned absurd these days in B'lore.
There are a couple of KSTDC ( state run ) coaches that take you round the city. You could check with the KSTDC counters for more info. They also have similar coaches that are operated to many other tourist cities in the state.
About shopping, if you are looking for Indian part/casual wear for u'rself and daughter , head to Commercial Street which is quite close to MG Rd.
You have plety options there. DCM will be reasonable + stcks good collections. Try the adjacent lanes( or Ibrahim Strt ) for good collection for your daughter. I used to shop for my 4+ yr old niece in those small lanes.
If you are looking for western outfits, you'll find some on Commercial St but i suggest head to Forum / Central / Garuda for better / branded options.
Letz c what others have to key in. Hope you enjoy your stay in B'lore.
Happy Holidays!