Start your visit to Hanover by rambling around the city centre and the Altstadt – simply follow the red line in the pavement from the main tourist office. Stop for a quick lunch at Markthalle, which has an international variety of food stalls. The line returns you to the Hauptbahnhof, behind which the long Lister Meile offers numerous restaurants and bars. After dinner catch a live performance at Pavillon.
On day two, visit the Herrenhäuser Gärten to meander through the international flora of the botanical Berggarten and the fountains and statues of the formal Grosser Garten. Exit the Grosser Garten through its eastern exit and walk into Georgengarten to the Wilhelm Busch Museum of caricature and cartoon art. Head over to trendy Linden-Limmer for dinner and drinks. If it's a weekend, you can end your night at a club in Steintor.
Hildesheim is only 30 minutes away by train, making it a perfect day-trip destination for day three. Alternatively, your options in town include exploring the lush Eilenriede Forest by foot or bike or taking some modern art at the Sprengel Museum then strolling alongside the lovely Maschsee lake, where you can end the evening with dinner at Pier 51.