Edinburgh is a compact and beautiful city. There is no better way to see it than to walk. Places are usually no further than 30 minutes walking.
Single tickets for Lothian Buses are £1.50 and are valid for only one journey. If you need to change bus, you have to buy another £1.50 ticket! Keep in mind that that you will have to give the exact amount as the bus drives will not have any change. Lothian also offer an all-day ticket for £4.00 that covers all buses (except sightseeing, airport express and night services) and the trams.
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*Times can vary depending on the weather and traffic.