With the exception of the 'meteor' style event, a tsunami wave isn't actually that high. In the Indonesian earthquake that caused the tsunami there, it's debatable if the height of the wave was over 10 feet tall. The destructive part came from the pure volume of water and the energy/strength it brings...anything not anchored in, is pretty readily relocated a long ways into shore. I doubt the water itself would ever down a skyscraper, however I could see a tsunami crashing enough debris (including houses) into the foundations of these buildings to cause enough structural damage to bring one down.
I have met travelers who avoided the initial wave on a 3 story roof top of a building that bore the brunt of the initial strike in the Indonesian tsunami in 2004....terrifying, but not that likely to kill. What made this tsunami dangerous was a complete lack of warning coupled with natural human curiosity...we saw the water heavily recede and came out to see whats happening. Correct response if you ever see an ocean's water recede into the distance is to get to high ground immediately, you're probably too late if you're on the beach seeing the water recede.
Surviving the initial wave is simply being out of this water flow and debris. In hills or in buildings is quite functional...trees have a potential of working as well, you just have to make sure whatever you're standing on isn't swept away.
However I do not believe that is the most dangerous part of a tsunami...it's the days after. Survivors find themselves stuck in standing water with very limited mobility, full of sewage and debris that have been washed up. Entering standing water is inherently dangerous as metal shards from what used to be signs and cars are quick to cut open skin. Once cut open, the wound is exposed to this sewage happy water and will likely become infected and toxic. Take Katrina and the impact flooding New Orleans had as an example here.
A city's water supply is most often underground, so the aftermath now includes a complete lack of drinking water (even worse if you consider most bottled water supplies are kept on ground floors). The majority of food (grocery stores) tend to be on ground levels as well, which is now covered in not so clean water.
So you're stuck, with likely a lot of other survivors, with very limited food and water...and absolutely no mobility that doesn't come with some serious risks.