I visited Lerwick in the summer of 2007, it was summer but still wet, cold and windy. We arrived very early in the morning from Kirkwall and unfortunately due to the connection with the Faroes, only had one day to explore the Shetlands, worse yet it was Sunday and Lerwick is officially the most religious spot in the UK, with practically everything shut. Despite these factors, we had a good time. We arrived at around 6am and meandered along the coast for a bit until something opened, it was distinctly grey but we spotted a seal which was some consolation for lugging around backpacks!
We walked the streets with not a soul to be seen before discovering an open cafe and ice cream shop, the proprietor was extremely friendly and welcoming and one hour later , we were not only knowledgeable about the island but knew what was open, what to do and had picked up a bit of a gossip too. If you opt for the Sunday visit, I reccomend taking your own transport to explore the islands a bit. After seeing enough of the town and being rained off, we headed to the superb Shetland Musem which is free on a Sunday. It informs the visitor not only about every era of the islands but also the way in which people worked. I found it fascinating and its one of the best, well laid out museums I've been to in recent years. We also had lunch there which was reasonably priced and nice.
On the way to the departing ferry, we stocked up on food at Spar knowing that it'd be cheaper than in Faroe Islands and Iceland, this proved to be an error of some proportions, as we had it all confiscated at the rather impressive ferr terminal by the strict UK customs. The reason for this is that both Faroes and Iceland have their own rare species that have supposedly had little contact with their average European counterparts, dairy and meat products are out of the question and when we went they scoured the ingredients of ever item in Scotland. Annoyingly, this is not enforced from the Danish or German connection to the Froes and you can also buy such products freely on the boat, so it all seems a bit pointless