A Multimuseo card (€10.50), available at the tourist office and select museums, is a good bargain for entrance to all of the state museums. Overnight guests can take advantage of the free TuttoSanMarino card, which offers discounts on the Multimuseo card as well as private museums, transport and selected shops and restaurants.
If you have an EU-issued SIM card, you won't incur roaming charges in San Marino unless it's from Vodafone Italy, which is the only Italian mobile provider yet to strike a deal with the republic at the time of writing. Otherwise look for the free w-ifi network 'Livein.SM Free WIFI,' which works fussily around the city centre.
Post Office Vital for sending those 'proof-you've-been-there' postcards.
Tourist Office You can get your passport stamped with a San Marino visa for €5 here (cash only). In 2020, the office is expected to move to Piazza Garibaldi 1, inside the new Museo Filatelico e Numismatico, which will re-open in the historic centre after closing in Borgo Maggiore in the 1980s.