Hey, good to hear from you again. Thanks for letting me know the budget that you had in mind, this really helps me narrow down the list for you. So here are some more options for you. What I have done in thrown in a mix of mainstream and boutique hotels, so that you get a good range to pick from:
If you are willing to pay a little more for your stay, then Casa Severina will be an excellent choice. It is a heritage hotel and an architectural endeavour. The best part is its calm and quiet location. The tariff if about INR 8000 per night. Even if you don't intend to stay here, do visit the hotel website and read more about it. It is an interesting read and once you are done, I am sure you will love the place and wouldn't mind spending that extra bit.
About hotel websites, I have seen that leaving the 5-stars aside, most hotels in India don't do a good job of the website. I do agree that this is probably the only point of reference you have about the hotel, but sadly the current situation is that hotels are just not that tech savvy.
That said, what I have done is that I have created a map which will give you an idea of where exactly these hotels are.
I am sure that from the above list you can find the right place for your stay. If you want more details, please do write back.
Have a pleasant stay!
Sneha.