The closest airport is Cologne/Bonn Airport. There is a bus (SB60) going from Cologne/Bonn airport to Bonn central station (Bonn Hauptbahnhof (Hbf)) every 30 minutes. Close airports are also (in alphabetical order) Dortmund, Düsseldorf, Düsseldorf Weeze, Frankfurt, Frankfurt Hahn.
The main train station is Bonn Hauptbahnhof (Hbf). For the train schedules you may visit bahn.de.
From the main station to the Mathematical Institute you may walk (about 15 minutes) or take a bus (lines 604, 605, 606, 607, stop "Kaufmannstraße").
Hotels (all of them within walking distance of the institute):
Suggestions for lunch breaks
Clemens-August Strasse (highlighted in orange on the map below), near Poppelsdorfer Schloss, has many options for restaurants and snacks.