Wonder of the World
If you only have a limited time to travel, then you are going to Agra to see the Taj Mahal. You know it. I know it. Everyone knows it. The Taj itself is impressive, though the grounsd around the monument make it seem even more so. Once you are inside the complex, a guide comes in handy as there is no explanation for anything. I also cannot overstate how bad the markets around the Taj are for souvenir shopping - you will definitely be overpaying for everything. Be aware that Agra suffers from similar pollution to Delhi (see my unfortunate photo).
If you have time to spare in Agra, there is a fort and a cenotaph you may be interested in, but these will likley be secondary destinations.
Arrival and Departure
You can get to Agra by bus or train, but if you have the budget and/or patience, I recommend geting a private driver or going with daily tour group. Agra is about 4 hours from both Delhi and Jaipur, and there are daily tour groups from hotels, hostels, and travel agencies that will include your entry tickets.