The Lal Bagh Gardens, the Malleswaram district for a vibrant atmosphere in the shopping area, Commercial Street for up market shopping such as Fab India, Bannerghatta National Park on the outskirts of the city, Raintree Cafe for wonderful coffee and cream cakes opposite Windsor Hotel - and for something different visit the People for Animals Sanctuary and offer them support for all the good work they do. Indulge also in the numerous restaurants and cafes offering cuisine from all over the world.
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For shopping you have commercial street, shivaji nagar - you can visit brigade road but little expense - just good for strolling around. Ofcourse other places to see would be Lal Bagh, Cubbon Park, Ragiguda Temple, Nandi Hills, etc. Remember there are plenty of places outside Bangalore you may want to consider - say like Kudremukh, Kuke (for worship), etc. So I would recommend you can buy a travel guide book and see what suits you based on your interests. Just make sure you have a mix of all types of places - so that everyone can enjoy the trip.