The east coast doesn't match the west for beauty but there are plenty of interesting places to visit for day trips. The nicer ones are on the Fife coast and it's probably a good reason for not having your boat based in Fife and travelling to it because you'll already be there! Sorry Sea Skills, no critisism intended.
As I said earlier, most of the harbours dry but nevertheless there are few within the Edinburgh area. Three hours either side of high tide is typical for access. Get a map...Travelling eastwards from Port Edgar (the marina) on the south side, there is a nice little harbour in South Queensferry, next is Crammond then Newhaven, Granton, miss out Leith docks then it's a good distance along to Mussleburgh, there's a small club and boat compound at Prestonpans with a slip but it launches directly into the sea with no protection, next is Cockenzie which is possible but probably not worth it then Port Seton which is useful with a protected slip. After that it a good distance along to North Berwick, best as a destination because there's a selection of eating places and reasonable shelter. Launching there is off the beach. A trip around the Bass Rock is always good and then further east still you leave the Forth and next stop is Dunbar.
On the north coast, starting again at the Forth bridges, there's North Queensferry, give it a glancing blow at most, Inverkeithing, worth travelling there to say you've done it, then Inchcolm (an island with a monastery) which is worth a visit though you may be charged, depending on season. Opposite is Aberdour which I visit often and I feel has some charm. Next is Burnt Island but it's pretty commercial, followed by Kinghorn, not much more than a jetty and a lifeboat, then Kirkaldy, do it once and on to Dysart which I also particularly like. There are some other small places further along then Methil docks and on to Lower Largo which is very tidal but worth a trip and there's eating at a place on the sea wall. Elie is next and a nice place to visit plus good eating; Sea Skills will be able to tell you more. Further along still there are various harbours some of them more fishing fleet places than pleasure and lastly there's Crail which is I also particularly like. If you want to leave the Forth area northward then St. Andrews is next and it too is a good place to visit. Like most of the other places, it dries. I'd better not forget the Isle of May which should definately be on your list and is accessible most of the time and it's an interesting entrance when there's an easterly swell, though you can land on the west side if you must. Off Edinburgh is Inchkeith with good landing and no one living there presently but lots of bird poo. Beware reefs, study the chart.
I think that's about it. Others will be along to fill in my blanks.
Regarding keeping your boat on the west coast, some folk do but you miss those times when the weather is crackin and you just need to get a fix of boating of a evening.
But, the west has beautiful scenery and, once there, you have access to a vast area pretty much all of which is worth doing. There are pros and cons which you'll need to consider.