I cannot find on the Regent website the current description of your time in Agra; so I cannot be too specific. However, I will give you my observations, for what it is (or ain’t) worth regarding your stay in Agra.
Fridays in Agra are somewhat different from other days, as the Taj Mahal is closed for maintenance (not religious services) that day.
However, as Pam T. mentioned some time ago on one of the TAJ threads, one can have a good view of the Taj Mahal from the Mehtab Bagh gardens directly across the river from the monument. We visited Mehtab Bagh on a Monday; and we were the only people there, aside from three Indian Army guards, who were sleeping next to the river (guarding that possible avenue of terrorist entry into the monument…). However, according to our guide, on Fridays the Mehtab Bagh location is very popular, since it is the best place in the city to view the Taj Mahal when the monument is closed.
In fact, the view of the Taj from the gardens is quite good, although without the lovely gardens and fountains that one sees when entering into the grounds of the Taj from the regular gates. The view from Mehtab Bagh is directly south across the Yamuna River onto the monument. It was prudent when we were there to sort of zone out one’s eyesight with respect to the river, which was quite low and quite repellent, and focus instead on the magnificent monument on the other side.
I am not sure how long it would take to taxi (or, for those of you with strong hearts, take a tuk-tuk) from the ITC Mughal because we visited the gardens in conjunction with a visit to the lovely little Itmad-ud-daulah mausoleum on that same side of the river and did not focus on the transit time. Certainly, the concierge at the hotel or your tour guide could tell you how far it is.
As Mehtab Bagh sits directly north of the Taj Mahal, in the afternoon the sun would be from the west, or onto one’s right when facing the monument from the gardens. Thus, the light would be the opposite from that in my attached photos. Please pardon the extreme fuzziness of the two photos. On the morning of our visit, it was very hazy (a common occurrence in winter because of fog and the wood smoke from the many households in Agra with no other source of heat or cooking fuel). Although we were delighted with the wonderfully cool temperatures during our visit, the trade-off was the heavy morning haze.
As for other attractions of Agra, a visit to the Agra Fort is definitely most worthwhile, and, as the palace where Shah Jahan (the builder of the Taj Mahal) was placed under house arrest by his son, has both a sad and a romantic aspect.
http://freddie98282.smugmug.com/Other/Taj-Mahal/i-k5Ssk3Q/0/M/Taj%20River-LCT-1-M.jpghttp://freddie98282.smugmug.com/Other/Taj-Mahal/i-kPtMmHb/0/M/Taj%20River-LCT-M.jpg