AAu's Tried-And-True Method of Not Getting Screwed1. Start with a phone call. Be sure you get someone who can actually do something. Front desk manager won't do it.
2. Assuming you get nowhere, send a letter. Letter should go to someone with clout.
3. Assuming you get nowhere, send a second letter. This one gets CCed to the Better Business Bureau.
4. Watch the issue be miraculously resolved.
Also:
DO NOT WAIT. You can lose some rights if you don't do things quickly.
$300 is not worth screwing over your credit. It really isn't. If the above doesn't work, you may also be able to negotiate with the hotel.
And BTW -- in issues of collection, it's not some special small claims court they take you to. There's a special process for such debts, and if the company chooses to pursue the issue, you can get a judgement slapped on you. This can lead to them actually freezing your bank accounts, plus a super-dark mark on your credit that will stay there for a long time. Getting such a judgement actually costs the company about $500, so most of the time, you're safe. However, a financial counselor I know told me that he is increasingly seeing judgements for smaller amounts. I don't know if this is BS or not, but why risk it?