Starved Rock State Park
If you've never been there, it's about 2 hours south of the city, which makes it perfect for a day trip or overnight getaway. Starved Rock sits along the Illinois River and has some truly interesting and unique geography, from bluffs overlooking the river to canyons and waterfalls. The trails are well marked and easy for dogs, and the leashed humans with them, to enjoy together. Adventurous sorts can splash in the creeks that run through the canyons and leap over obstacles. While the majority of folks park in the main lots and hike the sometimes crowded trails nearby, you can find quieter trails and canyons by parking in one of the smaller lots to the East. Unfortunately, the historic lodge and cabins in the park aren't dog friendly, but the lodge's large veranda overlooking the park seems to be. It's a lovely spot to take in the view while enjoying a snack, and perhaps an adult beverage, after a good hike. There are several hotels nearby in Oglesby and LaSalle/Peru that allow pets, so it's easy to find a spot to spend the night with your pooch.
If you've been to Starved Rock a million times, there are two other state parks within a 5-10 minute drive. They're small but definitely worth a stop. Matthiessen State Park shares much of Starved Rock's geographical features, but not its crowds. There's an easy path all around its central canyon and trails that take you right through the creek and waterfalls. Needless to say, waterproof shoes are a really good idea if you take that route! But for adventurous humans and pups, it's a fun, secluded and magical spot to spend an afternoon.
Across the river is Buffalo Rock State Park. There are scenic overlooks along the river and "effigy tumuli" which are large earth sculptures depicting several animals. They're not very well marked and pretty hard to distinguish, but it adds a little mystery while you take in the sights and sounds of the prairie. There are also two buffalo who live at the park in a fenced area. And what dog wouldn't want to tell his pals at the fire hydrant that he met a buffalo over the weekend?