How far off is the wedding? It may be best to wait until afterwards.

If you plan to buy it beforehand, make sure it's a home each of you could afford on your own in case one of you loses your job or gets injured or you break up before you're legally married. Also if you're both getting the mortgage, get your credit scores and see if one or both of you has to work improving that in the months to come. No large purchases (new car, etc) in the months before and pay down any debt you or your partner has.

If you don't want to get rid of the car, you'll have to cut something else out. I'd suggest the eating out and "shopping" as it sounds like this is non-essentials. Does your partner have a car? If so, can you just have the one car? This is dependent on if you live together, etc.

Also, find cheap/at home ideas for hanging out with friends. Host a potluck or movie night or something.