If Tromsø isn't far enough north for you, it's only a short flight up to Longyearbyen on Svalbard. This should be planned ahead, though, as flights vary incredibly in price. (http://www.svalbard.net). On short notice, your best bet is a flight-hotel package delivered from one of the tour operators up there.
Sommarøy is a fishing village south-west of Tromsø, with lovely, south-sea beaches and a fantastic view towards the island of Senja as well as the numerous islands belonging to the borough of Tromsø. No bus connection for day trips, except in summer.
Island Hopping in the north western archipelago goes with a local ferry from Belvik, a 50 minutes' from Tromsø. Islands visited are Vengsøy 100 inhabitants, Musvær 5 inhabitants, Risøy only inhabited in summer and Sandøy 3 inhabitants. Bring your own food, and lots of clothes. Sadly, there is no bus to the ferry or if there is, no bus going back..., so you need your own transport, which might be a rental car or a bike.
Lyngen (http://www.destinasjontro...) a peninsula 2 hour's drive east of Tromsø. The mountains rise 1800 metres dramatically from the sea. Plan well ahead, as there are few buses. Excellent destination with a rental car, though. Steindalsbreen is the most easily accessible glacier in the Lyngen Alps, found a few hours' walking distance from the road. It's a recommended sight, but hurry up - the glacier is disappearing rapidly! The walk up to the glacier is safe, but do not walk ON the glacier without a guide.
Senja is a bigger island just south of Tromsø. The area of interest is the outer side of the island, with a dramatic, rocky coastline dropping straight into the ocean. The fishing villages, notably Husøy, Mefjordvær, Bøvær, Torsken and Gryllefjord all enjoy fantastic locations. In summer, there is a ferry from Brensholmen near Tromsø to Botnhamn on Senja (http://www.senjafergene.no). The rest of the year, you drive inland through Nordkjosbotn and Finnsnes to reach the island. If by public transportation, plan well ahead.
There are very few buses into the immediate surroundings of Tromsø. It is difficult to find a bus that goes out of town in the morning, and back again in the afternoon.
