Late spring (May, early June) and early autumn (September) are the most pleasant times: warm, long days, beer gardens open, the Stadtwald in full leaf, the term still in session so the city feels alive. Summer can be lovely but many students vanish in July and August, and the city has a slightly empty feel.
Winter is cold and grey by central German standards, but the Christmas market on the market square in late November and December is one of the best in Lower Saxony — small, packed and informal — and worth a special trip. Major university events to time around: matriculation in October (boozy, busy) and the annual Händelfestspiele music festival in May.