BLR first. What else to see? What interests you?
Markets -
- Russell market
- City market
- traditional indian market selling most everything.
Can't think of anything else without knowing interests.
Mysore, in general has more things to do from a historic perspective. Not only the palaces, museum, zoo in Mysore, but excursions to chamundi hill, Srirangapatnam and the Cauvery river make it worthwhile.
While you can certainly do a train trip down to Mysore, i wouldn't advise it. As a point of reference, there are about 4-6 trains daily b'ween BLR and Mysore. This url
www.indianrail.gov.in/inet_metro_trns.html indicates there are at least 3 trains with an AC chair car. I know of the Shatabdi and the Tippu express. When traveling on these trains, keep a close eye on your belongings. I've known friends to loose stuff when they are deliberately distracted. One accomplice distracts, the other makes off with a laptop or ipod. So, beware. In general, its safe.
Rather than ride the train down, get a car with driver from the Park and drive down to Mysore. The BLR-Mysore road is far better now than it was a few years ago. The trip can be made in 3-4 hrs.
Plenty of interesting detours en route.
- Maddur for the vada.
- Closer to Mandya - you have Pandavapura (temple), Melkote (Sanskrit research institute, temple)
- Channapatna - for handcrafted toys (no match for chinese mass produced ones, but handcrafted and worth the stop).
With a car you can also use it to drive in and around Mysore.
OTOH, if you want to do some hiking, head to Coorg/Kodagu. The Park should be able to get you accomodations in Coorg for a night. the
Brahmagiri park has some trails. Or, ask for a local guide and hike to the Cauvery and back. Watch for Elephant ditches, those are big and deep.
Further south, you have the
B.R Hills, again with a temple and a forest for some hiking. No marked trails, but hire a local.
A little west of Bangalore en route to Hassan, you have Belur, Halebid and Southwest is Somnathpur, Talakad. Somnathpur's Channakesava temple is a great example of Hoysala architecture (as at Melkote, but far more intricate). So is Belur and Halebid. You can cover all these places in a day trip.