What are local LLMs good for?

There are various blog posts and YouTube videos out there whose basic content is: "Look, I installed an LLM on my shiny MacBook and was able to make it run". (Usually a MacBook, I think because 1. anything else makes it much more expensive to get a decent amount of GPU-accessible RAM and 2. I cynically suspect that part of the subtext of these is "look what a fancy laptop I can afford".)

What tends to be in shorter supply is much information about what these models are good for other than blogposts about "how I got a local LLM running on my machine".

I am in the market for a new laptop; it might be a Mac; I am curious what benefit I might get if I pay for more RAM and/or GPU cores in order to be able to run bigger models.

So, O glorious internet hive-mind:

If you have tried to run a local LLM on your own machine, what did you run on what hardware and what actually-useful things was it able or unable to do?

I am extra-interested in anything that would help me predict what extra value I might get from having a given amount more memory available to the GPU.

I am extra-interested in highly specific answers that let me know (1) some particular thing you were or weren't able to get the model to do satisfactorily, (2) whether it's likely that I'd agree with you about how satisfactory the outcome was, and (3) what hardware I'd need to be able to do similar things if I wanted to.

I'm interested in a wide variety of possible applications. (If you did some "running a large model on my own hardware" thing that isn't strictly an LLM, that could be interesting too. Image generation, for instance.)

If you did anything in the way of training or fine-tuning as well as just inference, that's interesting too.

I am not interested in general-principles answers along the lines of "AI is the future; if you aren't running LLMs on your laptop you're behind the times" or "LLMs are stochastic models and by definition can never do anything useful". (If you think one of those things, you might be right, but I get zero new information from the fact that someone thinks so; I already know that some people do.)

Thanks!