Take Amtrak to Providence and either rent a car there or perhaps someone might be able to pick you up at the train station to bring you to the hotel. I don't know how convenient the wedding part of your trip will be without renting a car. You might find you won't need it. I advise for you to check first.

You're coming next month which is not an inexpensive time to come here. Try looking at quikbook.com.

As for weddings, we've got 2 of them in September plus our anniversary. September is the new June.