The highway linking Agra to Delhi is actually a well made, brand new and is actually nearby to the international airport. It will be easy to get on to the highway from the airport and to head south.
My advice: get a car and driver (get a comfortable continental car), and you can be at the Taj in 2 plus hours. Spend an hour there and then head back to delhi with a further 2 plus hour drive. Getting to your hotel, depending on where you opt to stay will probably drag the journey a bit more as you get back to Delhi.
You could literally do the Taj in a day if you were careful with your time and had a decent driver without wasting time in a very dirty, polluted Agra.
Nothing else to see in Agra. We were happy to head back to Delhi after the day trip.