Volcán Rumiñahui is located in Cotopaxi National Park. Like Los Ilinizas across the Pan American Highway, it is long extinct. Unlike the Ilinizas, the major peaks on what is left of the crater rim are not considered separate mountains. The three highpoints are Rumiñahui Norte (4712 m), Rumiñahui Central (4631 m), and Rumiñahui Sur (4696 m). Because this mountain has no permanent snow and the route up Norte is no harder than a scramble, Rumiñahui is assured plenty of foot traffic.
However, because it is dwarfed by Cotopaxi just on the other side of Laguna Limpiopungo it is just as assured of never being a popular international destination. This, of course, is a shame. It is an excellent acclimatization climb with an exciting finish and epic views of El Corazón, Los Ilinizas, Sincholagua, and Cotopaxi.
Arriving to this mountain is nearly the same as Cotopaxi. Travel south on the Panamerica. A bus from Quito to Machachi is $2, Quito to Lasso is $2.50. From either of those two places hire a pickup for $20-$25 to Lago Limpiopungo within Cotopaxi National Park.
This is within Parque Nacional Cotopaxi and you will need a $10 permit. Camping is an additional $3. Camping is not allowed right at Limpiopungo however there are possibilities just beyond the lake on route to the mountain. Just be aware. Entire backpacks have been stolen from their "hidden" location offtrail in the paramo in this area while their owners were out climbing.
Like it's more well known neighbor, Cotopaxi, this mountain can be climbed throughout the year. The best climbing remains Dec-Jan or July-Aug however. July and August tend to be a little clearer but also have more potential for bad winds.
Camping is not allowed right at Lago Limpiopungo however there are possibilities just beyond the lake on route to the mountain. Just be aware. Entire backpacks have been stolen from their "hidden" locations off trail in the páramo and in unlocked lockers in this area/hut while their owners were out climbing. Also vehicles are not safe at the trailhead as the amount of broken glass attests.
The location is roughly between Quito and Lactacunga. For general route conditions, the South American Explorers probably have people that have climbed it recently among their members. They also try to keep a bulletin board updated with climbing conditions on the volcanoes in the Quito clubhouse. Generally, you can get some free route information by asking at the various climbing agencies too.