The New Haven register have revealed that shooting will begin on Thursday 28th in New Haven:

While Chapel Street will be closed to motorized vehicles, except for 1950s sedans and a motorcycle, for much of Thursday through Saturday, you’ll still be able to walk up the street and into Woolworth’s.

[...]

Because of the probability of changes in the filming schedule, the production crew will post the next day’s schedule each night on the city’s Web site, www.cityofnewhaven.com.

Shooting is expected to begin as early as 6am this Thursday until July 7th, omitting July 4th and Sunday 1st. The article goes on to highlight some changed minds regarding the Derby Avenue chase scene and a new scene altogether:

As of late last week, plans for Thursday were to shoot inside William L. Harkness Hall and the Yale Law School, and on the following streets, at least part of the time: College Street between Grove and Crown streets; Chapel, Elm and Grove between Temple and York streets; High between Crown and Elm; and Prospect Street between Trumbull and Grove streets.

[...]

One change the Paramount decision-makers have made is that they will not use a Yale practice field in the scene. “Their creative team decided that they’re not going to use Derby Avenue for the chase scene,” said West Haven Police Chief Ronald M. Quagliani.

Lamb said that part of the schedule will be filled with something new. “They’re creating a new scene, which hasn’t even been confirmed yet, so that’s going to go in there,” she said.

Wtnh.com are detailing a number of aesthetic changes you may come across,

All the shops along Chapel will be getting face lifts, the gallery’s, dress shops and restaurants.  Each could be in the background when filming begins next week.  Already Indiana Jones fever has begun and customers say you never know when you may see one of the movie stars.

Whilst New Haven are putting on the Indiana Jones and The Temple Street Festival. Check out all the details in the link, but proceedings include a free showing of Raiders of the Lost Ark and themed contests. All free of charge. It kicks off tomorrow, June 26th.