Rike Park is a green space across the river from the Old Town and where the Bridge of Peace extends from. It’s a nice peaceful area to sit and relax and gaze back across to the rooftops that extend from the river up to the Narikala Fort.
The park also has a number of noteworthy Tbilisi attractions. It has the Rike Concert Hall which is an interesting cylindrical, glass building at the northern end of the park. At the southern end, you’ll find the cable car station or aerial tramway that takes you up to the top of the ridge where the Mother of Georgia and Narikala Fort can be found.
If you want a coffee or glass of wine while you sit and relax in the park, then there are a few good spots where you can sit and order a drink, such as Summer Cafe or Art House.