Jyrgalan sits about 60km east of Karakol, roughly 1.5-2 hours by car on a road that's straightforward year-round.
A public marshrutka runs a few times a day from Ak-Tilek Market in Karakol — cheap, but on a fixed schedule that may not match your plans. A private taxi is the flexible option, and if you're coming specifically for a guided day trip or the start of a longer trek, a pre-arranged transfer skips the coordination entirely.
There's no need to overthink this one — it's a straightforward drive, not an expedition.