You don't climb the active Volcan de Fuego — it is genuinely dangerous and the exclusion zone is enforced — but you can drive to a series of viewpoints on the road north out of the city that put you within a few kilometres of the cone. The classic outlook is at La Yerbabuena, before the closure barriers, where on a clear morning you can see steam venting from the crater.
Local tour operators run half-day trips that combine the volcano viewpoints with the village of Comala, the source of the regional ceramics tradition. Mornings are best — afternoon cloud usually wraps the summit by lunchtime.