The Garhwal Circuit
It takes about six days to connect the Garhwali dots: Mussoorie, Rishikesh, and Haridwar. You can drive the entire way, or go partially by train. By road the trip is more expensive and tiring, but you can set your own pace and enjoy slightly better views—just don't drive at night. There are trains from Delhi and Dehra Dun (for Mussoorie) and Delhi and Haridwar. Catch the early morning Shatabdi (express) from Delhi to Dehra Dun, where your hotel can pick you up or you can hire a taxi for the 50-minute ride to Mussoorie. After two nights, hire another car to take you to Rishikesh, a journey of no more than three hours. Spend two or three days around Rishikesh and Haridwar, perhaps including some rafting and hiking, then catch the six-hour evening train from Haridwar to Delhi.
The Kumaon Circuit
This route is a gentle but colorful introduction to the region. Hire a car or jeep through a Delhi travel agency. Start by driving northeast from Delhi to Ramnagar, site of Corbett National Park. The drive takes six hours if you leave Delhi by 6 AM; after that, traffic near Delhi will extend the trip by several hours. When you've had your fill of Corbett, drive east to Nainital for a taste of modern Indian culture with a Raj flavor. From Nainital, go north to Ranikhet for golf or peaceful walks through the pine forests; from here you can make side trips to some important Hindu temples. Finish by looping back at the north end of Corbett, and perhaps by fishing on the Ramganga River. The trip takes from seven days to two weeks, depending on how long you want to linger over such diversions as searching for tigers.
The drive back to Delhi takes about seven hours but only if you leave the Corbett area before noon. If you don't, rush-hour traffic outside Delhi will again add an hour or four, and it's not a great idea to be on country roads after dusk. The appeal of the Kumaon region fluctuates with the weather, but March and December are the best times to make this trip. Corbett National Park is generally closed from mid-June to mid-November for the monsoon; Nainital and Ranikhet get snow in January.