Is CT considered the Italian Riviera? I think the towns just east of the France-Italy border are considered the Italian Riviera.
Nevertheless, for day trips from CT, people go to Porto Venere or more NW of CT towards Portofino, Santa Margherita Ligure, Camogli.
You can get to Portovenere by ferry. Depending on how hardcore you are about hiking, you can go up to the fort overlooking the city but there are more challenging hikes for elevation in CT.
There is also some trails between Riomaggiore and Porto Venere but I think those are long hikes so it wouldn't be a way to get to PV.
They offer some guided hikes or at least they used to over some of the CT villages, fairly nominal price.
There is also a very scenic path between Portofino and Santa Margherita Ligure but it's mostly flat so again, it depends on how much of a workout you want. When you get to Portofino, you can get more of a workout by climbing up to Castello Brown for views over the port.
If that's not enough, you can hike to San Fruttuoso or take a ferry there, though beware of the ferry schedules. There are also ferries towards Camogli. Not sure if you can hike from San Fruttuoso to Camogli. But you can take the ferry to the SW tip of the promontory and then hike from there to Camogli, where you can take the train back to CT.