There are many spots near mumbai in which you can go for camping. Camping can be done safely on spots such as Lonavala, Tungarli Lake, Valvan Lake, Rajmachi, Mahableshwar, Panchgani, Kashid & Phansad. You can try out letscampout.com (http://letscampout.com) for more options on camping near Mumbai. Rusticville (http://www.rusticville.com/) offers excellent hill top camping at Tikona near Lonavala.
It is very difficult to find good budget hotels in Mumbai. If you are a tourist or a business traveller, you may have to stay in South Mumbai, which is where both the business district and the touristy areas are. Lack of space means that even the cheapest hotel charges stratospheric tariffs. The state of public transport and traffic means that it is not really a good choice to stay anywhere else. In any case, things aren't much better if you are looking for hotels close to the airport. You should be looking at the Western Suburbs in that case. There are many guest houses at Colaba, where you find most of budget foreign travellers stay. Other budget hotels are found near railway stations, such as Dadar or Santa cruz, but most of them are absolute dumps. One safe and economical place to stay in Mumbai is the YMCA. Reasonably priced accommodations are available at the Colaba, Bombay Central, Andheri, and CBD Belapur Branches.
One inexpensive alternative is to live with a local family as a paying guest. A list of available families can be obtained from the Government of India tourist office +91 22 2220 7433 opposite Churchgate train station.
On the other hand, if money is of no problem, you can stay at the Taj in Colaba the oldest in India, the Leela Kempinski, the ITC Grand Maratha, or the JW Marriott Mumbai, Renaissance Mumbai Hotel & Convention Centre. Hotel listings are in the district pages.