How old is she?
For us, the most important thing was keeping the room dark enough and quiet enough if we were in a hotel with other guests, doors slamming, housekeeping carts, and neighboring TVs. So something for white noise is great unless you think you can depend on the provided clock radio for some static between radio stations (it's fine unless a station kicks in and out!). Clothespins for holding the curtains closed were a lifesaver (still are, for me!). If we rented a cottage, we made sure we had a small fan so there was a breeze in a closed room, and a piece of heavy fabric for hanging over flimsy curtains during naptime. We had a piece of fake leather from the remnant table (no light got through), a few drapery hooks, and the above-noted clothespins.
I'm not sure why you need a video monitor if you'll be in the next room but if it's small and makes you feel better, go ahead. If you have connecting rooms in a hotel, put a hand towel over the top to keep the door from closing on her side (your side has a knob). I agree with the comments below about the sliding doors. Also a doorknob cover to keep her out of the bathroom if she's a toddler, and one for the inside to keep her from pushing the lock if she's in there. If you're renting a cottage or are in an older hotel that may have venetian blinds, take come rubber bands or velcro plant stake strips to coil up the dangling cords.
Small travel games (age appropriate) that were new and unseen before the trip were great for car/plane rides, waiting times at restaurants, and hotel rooms with no amenities. Don't break them out all at once though - ration them!