I always tell my relatives to bring their own teabags when they visit. There have been no issues whatever about this; customs officials think this perfectly normal for visitors from the UK, and may even look askance at those who do not.
Tea is HUGE here. You can get Earl Grey with lavender accents and snobby French teas that even the French can't pronounce and things done with "'erbs" and fruit that don't even have any connection with the tea plant and white tea and green tea and it's all served iced, with or without ice, or hot in a glass, probably with lemon on the side. Ask for milk in it, and people will look at you like you just drop-kicked a kitten, but if you're lucky they might be able to find a sachet of powdered non-dairy creamer that's normally used for coffee.
"A mug, white, with one" has no meaning here in the US, because the incredible range of things they call tea precludes any such simplicity. Even being able to find plain black tea (which is what most Brits expect when we say "tea") will be a challenge, as most places don't even stock the stuff.
While you can get brands of tea that claim to be the same, at specialist places like World Market and such, odds are that you won't find a reliable source of tea that tastes as you are accustomed until you've been here a while (few years maybe).
Mostly, they're as much the "same" as cola canned in the UK, US, and middle east are the "same", which is to say, they have the same logo on the box but there it ends.
So bring a good stash of your own comfort drinks.
Also, bring a travel kettle that can work on 120v. Not only do most hotels not have a kettle in each room, but it's hard to find an electric kettle that actually works for any reasonable amount of money.
And don't use tap water to make the tea. I know, "don't drink the water" is so hackneyed travel advice, it's become a trope. But either buy bottled water, or get a very good water filter (which, thankfully, they DO sell here). Mains water is typically laced with chlorine and fluoride by law, to the point that you step out of the shower smelling olike you just stepped out of a swimming pool. So you will meet many Americans with thyroid issues (I never even knew thyroids existed, beyond a vague "heard the name", before I came to the US), and none of them have any clue why. Most assume it's genetic.
TL;DR: Don't drink the water. Bring tea bags. Bring a 120v kettle. And be prepared for the fact that the toilet paper is both a different shape, and not up to BSI Kitemark standards. Frankly, you might as well wipe your arse on a teabag. But that's another rant, for another time.
And don't get me started on the plumbing.