I agree with most of the advice given by Mell and Sam, may be not everything.
Yes, avoid mini skirts, not becasue people are sex demons here, but becasue they had a different upbringing. Actually, its no longer a threat as you can see many young girls wearning shirts, they are getting mini every year, though still not as europeon. People are getting broad minded.
Second, you need to take all that care that one must take when travelling alone, irrespective of which country it is.
Yes, Sam is right on hygeine, do not drink any water or eat anywhere. Your system will not accept. So, drink good quality bottled water like Bisleri, Kinley, Aquafina...these are easily available at retail shops.
One point, inspite of low hygeine levels the cases of food poisoning in India are less becasue we eat everything well cooked and hot. So, my advice is you eat from a place, which is considerably occupied as your chances of getting fresh food there are more and try and choose dishes that are served hot. Do not try your hand at cold cuts or cut fruits etc. Simply, eat what feels good thru eyes and nose, they are the best judge. First eyes then nose and then hands and then tounge. Follow the sequence and you will never fall sick of eating.
Mell is right about Internet cafe's. Do not use your Credit Card there too often. If you need to use CC online, carry one with a lowere limit. This actually is true for every country now as Cyber Crime takes ugly shape.
Last, my advice will be you travel to East of India first, it is amazingly and breathtakingly beautiful. I am talking of places like Sikkim, Shillong, Manipur, Chirapunji, Darjelling. From here you can visit Nepal and Bhutan. Then come back to India, may be Kolkata and take off to Varanasi, Agra, Delhi, Jaipur, Pushkar, Mumbai, Goa etc.
I hope I could add some value here. I will try and answer if there are more queries.
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