Well, you have to know your DM. The age of the DM, how invested they already are in the hobby, how much of a collector the DM is, and other factors can make many of these suggestions be less than ideal. Obviously, any DM is going to graciously accept any of these suggestions with thanks, but if you don't know your DM that well, but you want to do something nice for her this Christmas, her is my annotated buying guide from the poll:
Dice
This is a good, safe option, especially if you are on a budget. While most DM's will have lots of dice, having a few more never hurts. But my recommendation is to find less common options. There are always kickstarters for dice, so you could back some and hold on to them for gifts as many of the kickstarted dice go out of production quickly. If your budget is not so tight and you are felling generous, get some nice precision metal dice. The good ones can cost $20 per die, so even just a d20 or a pair of d10s will be appreciated. Even if your DM has invested in high quality dice, he likely doesn't have a lot of them and will appreciate a few more.
Game Master's Screen
Unless the GM is absolutely new I would say no, this is not a good idea. First, even a new DM is likely to have bought one of the "official ones" and experienced DM have probably put a lot of thought into which screen they use--perhaps even creating their own custom screens. Also, if your DM does NOT use a screen, that is likely due to preference, and your DM may feel pressured to use a screen when she prefers not to if you give one to her as a gift.
Rulebooks
Again, probably not, unless your DM is just starting out. Generally the DM is going to have the books he needs to run the game he wants to run. I would only give a rule book as a DM if I really knew him well and knew he needed or wanted it and was unlikely to get it before the time I'm giving the gift. Some exceptions would be a student or someone with financial trouble that wants to DM but can afford the buy in--maybe a group of players can go in together and buy a core set for him. Another exception is a DM who likes to collect RPGs. If you know a system that he doesn't have, you can get that for him. Again, Kickstarter can be good for this, so long as you know he isn't backing it.
RPG-themed Clothing
Good, if you know the DMs tastes and size. Many of my players and I wear "gaming" shirts on game day. Just t-shirts with usually humorous art and text on them. I would love receiving these, but I am hesitant to gift them, mostly because I am awful with sizing. One thing I do though, is that some kickstarters include t-shirts as extra stretch goals. I'll often buy a couple extra at different sizes to give to one of my sons or a friend.
RPG-themed apps for phone/tablet/computer
You really need to know your DM's preferences well. A D&D Beyond subscription could be nice, if the DM doesn't already have one. But if he already has everything in Roll20, would he use it? If the DM likes pen and paper, and doesn't like electronics at the table, an app if probably not a great idea. DMs that use a lot of electronic aids at the table likely already spent a lot of time trying different options and may not need or want to use another app.
Theme Music
Depends on the DM. For myself, I would rather a player take the role of game DJ. I've tried Syrinscape and just using playlists from Youtube Music or Apple Music. It just became another thing I had to deal with. Of course, know your DM. But I would be hesitant to give music or game-sound subscriptions to DMs you don't know well.
Miniatures
I think this is one of the safest option. Even DMs that only do VTTs, they can still enjoy miniatures for the occasional game where digital options are not available. It is easy to know if a DM can use miniatures. If they play with miniatures at least some of the time, it is obvious they can use them. If you get them one they aready have, they can still use them.
Terrain & RPG Decor (lamps, tables, wall-hangings, etc.)
Again, unless you know that the DM only uses digital battlemaps, I think terrain is a good option. If you don't know the DM get setting agnostic terrain in easy-to-store formats. Battlemap spiral binders, felt 2D terrain and maps, tile sets, and arc knight style 2D stand up terrain are all pretty safe options.
I would not buy digital terrain and decor unless I am sure what system the DM uses.
Other (explain in the comments)
Some other items that most DMs can appreciate:
- measuring sticks for physical terrain & minis
- laser pointers
- game-themed swag like d20-shaped mugs
- gift cards to a FLGS
- Amazon gift cards