Most (maybe still all) Delhi hotels and bars don't serve alcohol at night so that's mostly out of the question.

Delhi is not a city to hang out at night by yourself, and particularly not if you have luggage with you. And the airport is no paradise to wait at either.

A cheap hotel -- available near the airport (right next to the Radisson DEL hotel) or elsewhere in DEL -- for storing luggage and to shower up followed by heading to a nicer hotel with a 24-hr restaurant for eating a slow meal and milking a cup of tea for all its worth probably works. Free wi-fi isn't a standard at most of the higher end hotels in DEL and isn't standard at most other hotels either, so it might be a struggle to get online at a hotel/shop.

Another alternative is to arrive there and hire a car to take you straight to Agra and get a hotel there ... which will usually be cheaper even at the higher end. My concern about this "straight to Agra by road" option, particularly at this time of the year (with fog this month, but unlikely next month when you'll be there), is road safety.