Open GardensGardens you can visit

The gardens and grounds of this hotel in Perthshire, Scotland, are open, free of charge, to the pulic. There are several old "speimen trees, including Redwood, Tulip Tree, Douglas Firs and Western Coastal...

I agree - the Barbican is a real hidden treasure. Last time I was in London, however, the tropical indoors bit was no longer open to the public. Hope this has now changed.

How to get there:-

Travel Information
Car From Central London: Leave the M4 at Junction 3 and take the A312 going south. Drive straight over the A4 and at the A30 turn right.
Keep on the A30, past Hatton...

Beautiful house with loads to see inside (takes approx an hour) - huge gardens (more of a park really) - Glass House full of interesting plants & climbers (only downside was not enough of them are actually...

Excellent collection of snowdrops, from memory gardens are open Saturday and Sunday throughout February for the Snowdrops and other times of the year. Gardens are registered with the RHS Open Gardens...