Towers do not always have to consist of residential, offices, or hotel rooms. Many cities around the world have towers that exist solely as a landmark or tourist attraction. They do not always require a lot of space and can have a minimal (and usually beneficial) impact on the skyline.
Brighton (UK) is building a 531 foot-tall "skinny tower" that is only 13 feet wide called the Brighton i360. Once completed later this summer it will be the world's tallest moving observation tower. Given the tiny footprint of a tower like this, it could be located pretty much anywhere.
Since Downtown San Jose is burdened by height limitations, it would make sense to locate something like this just outside of Downtown. Somewhere in the Santana Row / Winchester Mystery House area or in Kelly Park would be ideal since tourists are already visiting those locations and they would provide amazing 360 degree views of the valley.
A tower like this looks extremely expensive but the cost is around $60 million at 531 feet. Levi's Stadium was more expensive than 20 of these and a shorter tower would be even less expensive to build. The cost is actually not that much for a landmark attraction that would help define our skyline.