Ok, having some actual experience on this, I think you can ignore most of what has been posted here, particularly all those "10K? No way! Ask them for 100K!" posts. It just doesn't work like that.
Two posts that do strike a chord with me are ChrisNorstrom's and LargeCompanies'.
Whoever said they will clone you if you don't sell is also correct. That means that whatever value your project may have now it won't have in the future once the competitors (plural!) start popping in.
It appears that you have already talked to them and figured what their motivations are, that's good.
Depending on how good your negotiation skills are (and I'll assume they're not very good, since you're asking here) and what your feeling about their offer is (whether they're lowballing it and how much) you could:
1. Ask them for a bit more (maybe 50% / 100%) and sell as-is, or
2. Take their offer and sell as-is, then
3. Offer them a limited number of support days at a fair day rate ($600-$1200?). This is where, after you get the money, you show them how your thing (which is now their thing) works, and
4. That should be the entirety of the agreement.
That means no code review, no technical discussion, nothing. They have seen what they have seen and they have named a price that's good enough for them based on the information they already have. They don't need any more than that and you are satisfied that it's a fair valuation.
Just to emphasise, if they are well-resourced enough and have enough of an interest in whatever your product is, and you don't sell it to them, they will copy it.
So you'll be better off selling it blind to them for whatever money they offered and then you just set up a new site competing against your own old code. See my point 4 above and don't sign a no-compete clause. Hopefully you're a good enough actor to play dumb and convince them the deal is not worth enough for you if you need to start lawyering up so you'd rather keep things simple.
All the above is based on actual experience.