If what you are seeking in a bike trail is diversity of views and environments, the Monon Trail is for you. It runs 27 miles from downtown Indianapolis north to the small town of Sheridan Indiana. There are many sights to see and places to stop along the way.
From downtown the trail is very urban and passes under I-65 and I-70 and through some residential neighborhoods. After about 6 miles the trail passes through Broad Ripple where there are plenty of opportunities to stop for ice cream, food, coffee, beer, and shopping. There is even the Bike Line bike shop right on the trail if you need something for your bike or just want to browse. I highly recommend grabbing lunch at the Public Greens and ice cream at BRICS.
The scenery changes a bit past Broad Ripple. The trail will cross over the Canal and the White River and wanders past city parks and neighborhoods. Right before 86th street is the Big Lug Canteen with outdoor seating perfect for sweaty bicyclists.
Next up is Carmel. Riding through Carmel requires some heads up navigation. I've never been through the area when it wasn't pedestrian packed. Again this area is is full of places to stop, rest, eat, or drink. There is even a nice linear playground right on the trail if you have the kids in tow. I recommend Bub's Burgers and Ice Cream for lunch, Union Brewing if you are just looking for a beer or Sun King Brewery for lunch and beer.
North of Carmel, the trail meanders through neighborhoods until it reaches the community of Westfield. My favorite part of the trail is also the newest part of the trail. From Westfield until the end the traffic thins out and the trail passes through wood lots and farms all the way to Sheridan. There is a city park in Sheridan, a nice place to take a water break before beginning the ride South.
There are plenty of parking lots with water and restrooms along the trail.