Will I be able to see anything recognizable on Alcatraz from shore? Like from Pier 39 in San Francisco.
Yes. Assuming a reasonably clear time of day with visibility of a couple miles (which is not at all a given, see comments about fog above), the island and the prison building are easily visible from along the northern waterfront or from a building with a view of the northern waterfront.
For example, let's Google Street View ourselves to the Pier 39 area. That island with the white building is Alcatraz. The big building in the middle is the prison. Just look out over the Bay and there it is. There should be some coin-operated binoculars around if you want a closer look.
I'd embed the Street View photo, but since you want the "element of surprise," I'll link it instead. I've provided some annotations.
You can see it from much further away too. Here's the view from the Top of the Mark cocktail bar at the InterContinental Mark Hopkins hotel on Nob Hill. A building obscures half of it, but there's Alcatraz right in the Bay.
Or go all the way back to Twin Peaks, and you can still see it on a clear day, albeit from a greater distance. That's about 5.5 miles.
Wondering if the weather is cooperating? There are a number of webcams around the Bay you can consult. There's supposed to be two on Alcatraz itself, though they aren't working for me at this moment. Alcatraz is clearly visible on this webcam at the South End Rowing Club (despite the name, it's located on the northern edge of the city) when it's clear, and obscured by fog when it's not. Note that this camera moves around on its own sometimes; when it's pointed at the prison with the ship's masts in the foreground, you have the right image.
With the naked eye from the shore nearby the island is visible, though without much detail and subject to weather conditions (eg fog) etc.
Being a small island and 2.5 miles offshore a small coin held at arm's length onshore would probably be just about enough to obscure the whole island. Though It does not occupy much of the area of sight, from there at least a building and a tower should be discernible, together with some other details, even if it is not clear what these other details are.
With vision assistance (eg binoculars or camera) the island might well fill the field of view without loss of much definition.
For me a visit to the island has very little appeal but seeing it from shore is something I would like to do. The cost/time/administration involved with a tour just does not seem worthwhile to me but I feel a sense of significance and marvel achievable just by live observation from a distance. Prisons are mostly four (probably drab) walls and a lot of security the world over. Alcatraz's USP was its location in the bay and how effective a mere 2.5 miles of water was as a 'moat'. That can be seen when looking towards the island almost as well as when looking from the island.
I have not posted an image because the OP has indicated a desire to keep sight of it as a surprise until there. However photos can easily be found on Google Earth that indicate how much can be seen from shore.
Besides the view from shore at the various points mentioned by Zach, if you go to the Alcatraz ticket office, you can also see quite a large model of the island. This would allow you toview the island and be able to identify exactly what parts of it you're seeing.
I've been to Alcatraz twice and I definitely think it's worth a visit. It's so striking being on the island and seeing the locations you would be aware of from the movie.
If you really want to get a feel of the idea of escaping from the island, you can sign up for a swim from Alcatraz (actually from a boat just off the island) to the mainland. Here's one company that organises them. It's on my todo list.