Do most of the hotels in Delhi have shuttle buses to take guests to the popular tourist sites within the city? If not, do they have drivers that you can hire to take you instead of the bus or a taxi?
There are no hotels which provide a shuttle bus service to visit tourist places in the city, but some hotels can organize a city tour service in a car. I would check the prices from outside as well because sometimes hotels do overcharge for such services. The other option I can suggest to you is getting the HoHo bus, this is a bus service which takes you to all the major tourist places in the city and you can choose form either a one day or two days tour. Its an easy way of traveling, affordable and most comfortable.