This is probably an area where I am Very Rude, as about 90% of my socialising involves going to other people's houses and eating their food. I tend to solve the problem via the Hugh Grant approach, though, as I always talk too much and sound daft. But generally starting with "it would be nice to see you" is a good feint, and then the other person can make vague "yes, why don't we have dinner at some point" and I can say "Do you want to be dragged to Coventry or should I descend on you again" etc etc.

In general, I prefer honestly laying my cards on the table about what is easy and difficult for me to do, and would prefer the other person to do the same, over trying to be polite. Politeness works by knowing what is most convenient for the other person and making it happen gently without them knowing. The world is getting so confusing with the diversity of lifestyles, eating requirements, people who drive, people who think it is morally wrong or unpleasent to be driven around etc that I don't think I can make the guess of what is most convenient for anyone except maybe closest friends.