In general, the dress code for a party at a restaurant is similar or more formal than the typical dress code for the establishment. Never dress less formally than the typical restaurant attire and to be cautious dress a step nicer. Dinner parties are usually occasions where people dress up, so you don't want to look out of place.
For a nicer restaurant you will want to wear a pair of dark pants with a long-sleeve buttoned down shirt. Matching shoes, socks and belt is also required. For less formal occasions you can wear brown shoes and khaki colored or other light colored pants. sport coats are often a good idea for a nicer dinner.
Dress at or a step nicer than the restaurants typical dress code
Consider who else is attending the party
It's easy to take off a sport coat if you end up looking to formal