Is the height of Karin Tower ever given?

[Rocketman]

I wasn't aware back then they put rocket engines in aircrafts that could lift them to extreme altitudes. Since initially rockets are meant for space, hence why we have space rockets here (none of which designed for traveling in high altitudes in the Earth's atmosphere like a luxury cabin).

Me 163, 1941, the world's only rocket-propelled fighter plane. It could reach 12,000 meters up. By 1946, the Bell X-1, the rocket-plane that first broke the sound barrier, could fly to 27,000 meters up.

And rocket-propelled planes exist in DB, see General Blue's aircraft, or the one the crew ride in to assault the Red Ribbon base.

[Perfect]

I wasn't aware back then they put rocket engines in aircrafts that could lift them to extreme altitudes. Since initially rockets are meant for space, hence why we have space rockets here (none of which designed for traveling in high altitudes in the Earth's atmosphere like a luxury cabin).

Me 163, 1941, the world's only rocket-propelled fighter plane. It could reach 12,000 meters up. By 1946, the Bell X-1, the rocket-plane that first broke the sound barrier, could fly to 27,000 meters up.

And rocket-propelled planes exist in DB, see General Blue's aircraft, or the one the crew ride in to assault the Red Ribbon base.

As it's been stated, the series logic doesn't correspond with the logic in the real world (most of the time).
For all we know, General Blue's aircraft couldn't reach such a height, there's nothing that justifies it can or can't.
Not to mention the "rockets" that power it may or may not be that powerful (certainly not as powerful as the ones used to launch astronauts into space; ie what I was pertaining to). Not to mention the designs for vehicles are quite different than they are here.

[Bussani]

Karin says even a rocket would be repelled, so no.

Yep. That was my point. I'll transcribe a bit of the conversation for people who don't have the volume.

Karin: "The sanctuary floats high above this tower."
Goku: "F-floats?!"
Yajirobe: "This just keeps getting stupider-- See?! There's nothing up there to see!"
Karin: "That's because it is much, much higher."
Goku: "All right! I'll try to get there on Kinto'un!"
Karin: "Kinto'un will not be enough--it can't go any higher up than this."
Yajirobe: "All right--then I'll go steal you a rocket or something!"
Karin: "Heh heh heh... Just as useless... Even if you could get close to the sanctuary in such a thing, you'd be repelled."
Goku: "Then what do I need to do?... Even I can't jump that high..."
Karin: "Ho ho ho... Goku, my lad, you are truly blessed by fortune. The magic staff you possess shall take you there."
Goku: "My nyoi-bo?!"
Karin: "In its origin, the nyoi-bo was the staff that connected this world and the sanctuary. A very long time ago, that Muten-Roshi rascal kept pestering me for it. And since I thought no one worthy to visit the sanctuary would ever show up, I finally gave in and lent it to him."

That's where the idea that Nyoi'bo is what makes it possible to reach Kami's place at all comes from. Karin makes it sound like it's a bridge that enables any travel there. And apart from when Goku has Nyoi'bo with him at the 23rd tournament, it's always shown to be connecting the tower and the sanctuary after that point.

[Dayspring]

I figure she wasn't repelled because she was needed by the guests already there, or that Kami's absence means the place has no reason to repel anyone anymore so it doesn't.