There's plenty of parking, it's just not always easy to find. The majority of downtown stores are located on Lincolnway between Lafayette Street and Morgan Blvd. They're mostly on the north side as the County Courthouse is in the middle on the south side. There is lots of street parking, but it's often hard to find and then trying to get into a spot with traffic coming up from behind can be nerve racking.
Instead, find a parking space. Coming from the east, ther parking is a half block north of Lincolnway and Morgan (on Morgan) and a half block up (there's a hill) on Lincolnway. (Avoid the 'Round the Clock' parking lot - unless you're eating there.
From the west, you'll need to go a block north to Jefferson St. It's one-way (east bound) and there is a large parking lot on the north side from Napoleon to Lafayette. (Again avoid the Centier Bank lot on the south side (unless you bank there)). Further up on Jefferson is another lot at the corner with Washington. This is a good spot for west end shopping or going to the Chicago Street Theater.
If you come from the south up Washington Street, the best lot is a block west on Lafayette St between Monroe and Indiana Ave. It's also used for the County building across Lafayette street. You can also find parking to the southeast at Michigan and Indiana.
Of course, there are many lots for private business' and street parking.
Northwest Indiana funnels nearly 50% of the east to west (and west to east) traffic in the country through this area. This includes railroads. Trains are heavy (up to 20-30 tons per railcar) and long (average 2 miles-3.2 km). They take over a mile to stop. Don't cross against the signals. More than one driver has discovered that you're likely to be found dead at the wheel a half mile down from the crossing. Normally, it's only 5-8 minutes for a train to pass. Enjoy the different types of railcars. Guess where they're going.
Or take the roads that pass above the tracks --> Campbell St on the west side of town and SR 49 to the east.