I was able to tour inside Buckingham Palace in 1994 when the Queen first opened it to the public to raise funds to rebuild Windsor after the fire. I didn't think the outside was all that impressive, especially since I knew that Nash had remodeled it for George IV in the 1820's - I had expected more. What is inside makes up for whatever is lacking on the outside in terms of opulence and over-the-top decor. I can't imagine being a child inside the palace - priceless pieces of furniture, gold inlaid stairs and all kinds of other things, priceless art objects and paintings and portraits, mirrors everywhere.
We weren't allowed to take pictures anywhere inside or even in the courtyards or the lawns. You can buy postcard pictures of the rooms you were able to tour though. As far as I know the palace hasn't been opened to the public again, but with all the anti-royal sentiment and use of tax pounds, it probably will be (or has been and I never noticed). The Queen Victoria Memorial at the center of the traffic circle is a good place to sit and look at the Palace, watch the tourists, watch the guards not move. The changing of the guard only takes place every other day, at 11:30 a.m. but get their early so you can see.