Edinburgh is compact, bijou and easy to navigate.
The centre of Edinburgh is built in a grid system so with a map and a pair of good walking shoes Edinburgh is your oyster. If the weather drives you to alternatives then there are many.
If you are going from A to B flag down a black cab. They are the ubiquitous black ones you will see in many European cities. When the orange light is on, on the front of the cab, this indicates it is for hire. Put your hand up and it should slide effortlessly to a halt. If it is pouring with rain or you are starting off from a hotel or flat you can call ahead and they will be with you in a matter of moments unless you're travelling during peak times like Saturday nights and rush hour. Also, just ask any by-stander where the nearest taxi rank is, they are dotted all over the city and chances are there will be one close by.
Lothian Regional transport has many buses which do a great job. If you have an iPhone there is an app available to keep you up-to-date when a particular bus is due to arrive which means the days of standing at bus stops, losing the will to live, with the wind whistling through you are happily a thing of the past. www.lothianbuses.com
I would avoid driving in Edinburgh: well I do and I live here! The centre is not big and there are numerous one way, dead-end and bus and taxi only lanes which are stressful to drive as a local, let alone a visitor. In the event you do manage to navigate your way to your destination courtesy of your satnav and a wing and a prayer there is more chance of George Clooney appearing in front of you in full highland dress to take you for a pint than being able to find a parking space. I would say they are like gold dust - but gold dust is far more readily available to be honest. Leave the car behind.
Open Top bus
Directly opposite Waverley train station is the standpoint for this perennial favourite: the open top tour bus. I am a huge fan. It is the ideal way to get your bearings of the city whilst you are fed interesting and relevant information by the onboard guide. Quirky, entertaining, and some buses offer horrible history sound tracks for kids to follow on their headphones. This is a great way to see Edinburgh. You can jump on and off the buses all day if the mood takes you and you will learn far more in an hour than you would reading reams of paper for days. They have lots of different tours, some including boat trips, vintage buses and all in deals with attraction tickets. A good read of their website should help you decide which one is for you. Costing for the open top tour as a starting point is Adult £12, Senior/student £11, Child (5-15) £5, Family Ticket (2 adults up to 3 kids) £28. www.edinburghtour.com
If anyone tries to hire you a bike tell them to sling their hook. Driving here is bad enough; cycling is only for the hardy and mad. There are big hills and too many cars. This is a holiday after all, not the Tour D'ecosse.
Trike Tours Scotland
Not so much easy rider more easy chair rider. These are great fun. Sturdy trike motorbikes with driver will take you around the city – all you need to do is get in touch and tell them where you want to go and what you want to do. Really a hoot. Highly recommended. Cost is from £55 for an Edinburgh Tour for minimum two people which lasts 1 hour 20 minutes. They have a variety of longer tours too including a whirl out to The Forth Road & Forth Rail Bridge, a whisky trail including distillery in East Lothian and many others. www.triketoursscotland.co.uk
These little beauties turn up in the warmer months and whizz round the centre of town. Thighs like tugboats the guys who cycle them. They are fun to do and a bit mad. I have flagged one down on many an occasion but do be aware they can be dangerous if someone is acting the goat.