As the other answers recommend, look at the comps. Figure out what the unit is really, truly, worth. Then that's your maximum figure.
Now, you say you wouldn't pay more than $270,000. You don't say whether that's based on the comps (in which case that's your ceiling), whether that's based on what you can afford (in which case, that, too, is your ceiling), or just a gut reaction (which isn't as relevant here). But let's say $270,000 is the absolute ceiling either because of comps or what you can pay.
There's a tendency in the United States to "split the difference." A bad way of negotiating, but widely accepted. So, if you put in an offer at $250,000 and the seller wants to "split the difference," you'll end up around $280,000. And that's higher than your maximum. (Doesn't always work that way, but it does surprisingly often.) So, to answer your specific question, an offer of $250,000 might not be too low. Instead, it might be too high.
Would it be a "slap in the face" to the seller? Who cares? It's important only if you love the unit and absolutely want to keep negotiations going with the seller. If you've got a price, then negotiate in order to get your price.
Now, some very good agents here will have another strategy: Make an offer, back it up with as must documentation and justification as you can, and make it clear that your offer is your "best and final" one. A "take it or leave it" offer, but supported by enough data to fully justify the offer. And that strategy is definitely something you should consider. I prefer the first approach, but more agents will go for the second.
In either case, though, don't worry about insulting a seller. It's your purchase; it's your money; it's your home; it's your finances.
Hope that helps.