How long to see the main sights in Tromso

I'm planning on stopping over in Tromso on my way to Spitsbergen. At the moment, I'm planning on arriving in Tromso around 10am, and leaving the next morning. Is this long enough to see the main sights? If Tromso absolutely deserves longer than this, I can catch a later flight to Spitsbergen (but would rather take the earlier one - I'll already be jetlagged out of my brain).

A whole day should give you a decent chance to see the town. You should visit Polaria and Polarmuseet before heading to Svalbard.