That small dormant volcanic vent is called Binintiang Malaki and its just a small part (northwestern tip) of the Volcano Island, or real Taal Volcano.
How to get there (to the real Taal Volcano)
The jumpoff point to the Volcano Island is in Talisay, Batangas. It is that lake side town you see at the northern shores of Taal lake if you are in Tagaytay. There are several options going to Talisay via public transportation:
1. via Tanauan (ride buses bound for Batangas City, along Taft Ave in Manila) then ride a jeepney from Tanauan to Talisay
2. from Tagaytay, there is a winding road down to Talisay. There are jeepneys plying that route. The jeepney terminal is on Ligaya Drive.
When you reach Talisay there are lake resorts that offer banca rides to the Volcano Island (prices vary from Php1,500 to Php2,000). The banca ride is just about 30 minutes or so. You'd be surprised to see that there is a small community at the northern shores of the Volcano Island (talk about living in a danger zone, Taal is an active volcano). From there you can hire a guide and some horses if you prefer do it the Korean way hehehe.
The hiking trail is very manageable, but since there are no shades be ready to get real sweaty :). It is also very dusty especially if a group of 10-20 horse mounted Koreans passes you. (hey I've got nothing against Koreans, its just that Koreans comprise more than 90% of Taal volcano visitors nowadays. Some of them even tried building a spa resort near the crater).
Along the way (and especially near the top) you'll see (and smell) occasional steam hissing out from small cracks on the ground.
The view at the top is really marvelous. Its best to enjoy it by sipping that outrageously priced fresh buko juice (or softdrink) they sell at the peak. Yes, there are a couple of sari sari stores there.
Trivia about Taal Volcano and Taal Lake
1. the crater lake is on a volcano which is also in a caldera lake (Taal Lake) on top of an ancient volcano.
2. The Taal Lake is home to the tawilis, the world's only fresh water sardines. The fish is endemic to this area.
3. Taal Lake is also home to one of the world's rarest sea snakes, Hydrophis semperi.
4. Bull sharks, Carcharhinus leucas, used to be part of the lake's once-diverse ecosystem. They were hunted down in the 1930s