Sure this is a really obvious question. Is there a table somewhere which shows appropriate ability check DCs by level or by adventuring tier? I'm sure htere is and I'm just blanking on it.
There isn't one. 5e assigns DCs according to the task attempted, regardless of who's doing the task or what level/abilities they have. It's technically not even based on the task, but the specific action, so it's not technically correct to assign a DC to a wall to climb prior to a PC trying to climb it, although assigning static DCs is a common shortcut. Instead, the PHB has a list of common DCs by difficulty of the task (as determined by the GM), which are:
Easy.................................DC10
Moderate......................DC15
Hard................................DC 20
Very Hard......................DC 25
Nearly Impossilbe......DC 30
The reason for this is because of bounded accuracy -- the most the non-expert will be able to achieve with an ability check is +11, and that's after 17th level, with maximum ability, and proficiency. So, this character would fail about 40% of the time at a hard check (DC20). However, on the flip side, that same character could have a -1 in a different ability check, making a hard check (DC20) impossible. The expert can get up to +17, but they're an expert, and really should only be challenged by very hard or nearly impossible checks.
Now, if you're party can routinely leverage Bardic Inspiration or Guidance, then this gets skewed a bit, but that's really a matter of how easy is it to anticipate a challenge and leverage those abilities.