Joliet Union Station is a good place to train watch....lots and lots of BNSF freights, Metra commuters on both Rock Island and Heritage Corridors, Amtrak Lincoln Service and Texas Eagle trains, and if you're lucky, an Iowa Interstate freight train or two. The station has its own police substation and the local officials are informed about railfans and their needs. I've never seen any trouble, just stay on the platform and you'll be fine. In the morning, there's a business selling coffee, juice, rolls, etc. on the ground level of the station. There's also a bar/restaurant in the building. Just across the street is the Joliet JackHammers baseball stadium, visible from the platforms on the BNSF/UP side of the station. There are restaurants and fast food places in the adjacent downtown, although most may only be open on weekdays when the neighboring court building and county offices are open. There's a casino/hotel/restaurant/bar complex about three to four blocks from the station. If you're driving,parking will be tight on weekdays. There are several commuter lots that fill up on weekdays, a pay lot adjacent to the courthouse and metered street parking. All in all, a good place to spend the day.
Railroad sights in Hammond are less centralized. There's the Amtrak station area on the north end of town, featuring NS, EJ&E (oops, CN) and Chicago Short LIne freights and all Amtrak trains (except the Cardinal) headed east. The Horsehoe Casino with restaurants/lounges is adjacent to the Amtrak station.
Further south is the South Shore station, with an adjacent CSX freight line.
STill further south in the old downtown are the Ns (former Nickle Plate) and Indiana Harbor Belt freight lines.
There shouldn't be any problems at the Amtrak or South Shore stations, although the Amtrak station is somewhat isolated, with only a few trains stopping. The station is unmanned. The South Shore station has a ticket agent and a news/refreshment stand, along with other neighborhood businesses. Parking will be tight on weekdays.
The downtown area is slowly rebuilding and I'm not sure of the attitude of the NS and IHB police to railfans.
All in all, I'd vote for Joliet. Take the Metra Rock Island down and spend the day. The Metra Heritage Corridor runs only three trains the rush hour direction on weekdays. You could also ride Amtrak to and from Union Station, but the fare is considerably higher than Metra's.
Have a good day of railfanning.