,hi linoy
if you are landing in mumbai and from there you taking flight to banglore , why not to take flight from mumbai to cochin and if you booked alreaddy then no problem from banglore you will find good way to go any where with flight, train and bus. i would like to recomended you a place from banglore you can visit hampi which is nice and from there you can move to goa. this is one option and other if you like to make little long trip and spend some time with big city then you can go from banglore to maysor and from there you can go to kodaikanl (hill station) and from there if you like to spend some time with nature try to go to munnar and from there you can reach cohin easily .
dont worry to stay in cohin just cheak hodu.co.il there is category of guest houses. here you will find place to stay according to your budget.
and in cohin you can visit NET FISHING, SYNAGOGUE, BEACH(BUT NOT FOR SWIMMING) , KATTAKKALI DANCE AND CITY.