Some men really seem to push for this but I prefer a drink for a first date or a coffee - something low key so that if its a no, no not much is lost.
If you do go on a lunch or dinner date, who pays? My experience has been that I try to pay for myself but the man always insists on paying. I had one situation with a man where he was upset by my attempts to pay for myself. Then I started wondering - are there men out there who actually stick the woman with the entire bill????
I think that in an age where we want women to be seen as equal it doesn't seem to make sense to expect the man to take care of the whole bill. But generally I think dinner dates for a first date are a bad idea.