There is a small amount of parking in the park itself, so be sure to give yourself plenty of time to find parking. There is a small parking lot and some spaces along the the one-way street that goes around the green space. There is also street parking along Baseline Road north of the park. You can also park on any of the neighborhood streets north of the park.
Avanti validates parking if you park in the 1434 Spruce St garage nearby. It's privately owned though, so it's going to be more expensive if you don't want to mess with validation. Parking validation can be done when you arrive at Avanti at the host stand. City garages are free on weekends and the closest one would be on 15th and Pearl Street.
The Travel section of this site outlines a couple different options you have to get reliably from the airport to Boulder. I would recommend even if you are renting a car to book it in Boulder because the rates will likely be preferable than renting it from the airport location.
In addition to your AirBnB and VRBO options, we've outlined a few unique, local lodging options on the Travel page if you're curious. Otherwise, there are a couple Hiltons and other chain hotels in the area.
We will not be having a registry, and the bride will not be having a bridal shower. We don't want anything other than your company :)