The Holzhausenpark, the Grüneburgpark and the Palmengarten (the latter with entrance fee) are summer fixtures among Frankfurters. Especially, the Palmengarten and the adjacent Botanischer Garten (the latter only open in the summer) should be must-sees during a weekend visit. The Palmengarten's 19th century glass palace houses a beautiful palm tree garden with other exhibitions in the offering. Definitely go by the Siesmayer Cafe with the excellent, but decadent Siesmayer Torte, as well. Old money (i.e. villas, sports cars) can be witnessed in the charming Holzhausen- and Grünebrugparks. Now the university has officially moved in right next to the Grüneburgpark, so go ahead and visit the spectacular campus. Also, the Günthersburgpark in Bornheim (not that far away from the charming Berger Strasse) is one of Frankfurt's favorite family hangouts. 

 Although not so much a park, the "Museumsufer" (meaning the Museum promenade along Main) is one of the nicer river embankments in Germany. Especially the "Südseite" (the southern side of the Main) in Sachsenhausen makes for a perfect leisurely stroll. Parallel to the embankment runs  Frankfurt's crown jewel or "magnificent mile", the Museumsmeile, which is a collection of 10 museums with recommended cafés. Great views of the skyline, picknicking/running along the Main or simply taking in the cultural highlights in the high-brow museums such as the Staedel (with great impressionists), it's your choice.

 For more information, here is a link to information about:

Frankfurt am Main Parks & Gardens Info