3 or 4 days is sufficient to fly to DEL, and go down to Agra. You can see a lot in Delhi if you go to one of the official government tourist centers (there's one at Connaught Place) and hire a car & driver. About 2.5k rupees a day includes driver, gas, tolls, etc (everything except tip).

By hiring a car, you'll be able to handle Delhi solidly in 2 days: Humayun's tomb, Akshardom temple, India gate, lotus temple, Qutub Minar, Lodi gardens, outside of Red Fort (no need to go inside if you're also going to Agra Fort), Jama Masjid etc.

Hire a driver to go down to Agra. It'll save a lot of time and hassle. You can leave Delhi one evening, grab a hotel, and go to the Taj Mahal the next morning. In and around Agra, there's only two other things to see really. The Agra Fort is a quick 45 minute tour. Then, a fairly long 30+ minutes outside of town is Fatehpur Sikri, which is impressive and definitely worth seeing. You can drive back to Delhi and make it back by mid-late evening.

Jaipur is a great city to visit as well, but with 3-4 days, I don't think it'd make sense to pull that off.

Edit: BTW, Holiday Inn is considered a 5 star hotel in Agra