Some questions about my possible trip

Jirisan is quite a large park by Korean standards and so it has a few different access points. Getting there all depends on which area you want to go hiking in.
Here is a link to Korea National Park's Jirisan hiking section (in English). It has maps of each of the most popular hikes, as well as their distance and usual hiking times.

[http://english.knps.or.kr/Experience/ParkList.aspx?MenuNum=1&Submenu=Npp&Third=HikingCourses&Fourth=01&ParkDiv=10&HikDiv02=01]

However I haven't hiked Jirisan yet so I can't recommend any hikes there.

As for Gongju and Buyeo, again it depends on where you are in Jirisan, but your best bet is probably to get to Daejeon and then from Daejeon there are frequent buses to both cities (especially from Daejeon's Seobu Bus Terminal in the southwest of the city). I've been to both cities and they are both worth checking out for a few hours.

Jason

Name a specific town/access point of Jirisan National Park. Without it, it's no different from asking 'How do I get to Nevada Desert from LA?'

I want to go the western part of Jirisan probably Hwaeomsa Temple and around, so Gurye is best for that ? Hopefully with this added info I even get a better answer (Daejoen has more than one bus terminal is suppose from #1 answer ?).

Yeah, the main bus terminal in Daejeon is called the Dongbu Terminal on the eastern edge of the city. The Seobu Terminal is much smaller but many of the buses to Gongju and Buyeo leave from there because they are west of Daejeon. You can take city bus #201 (leaves every 10 minutes or so) between the terminals. It stops just out front of the Dongbu Terminal but I don't think you can see the Seobu Terminal from the bus because it's just off the main road, so you'd be better off asking the driver or another passenger to tell you where to get off.

From Gwangju Airport, take the unnumbered airport limo bus to Gwangju Bus Terminal, commonly referred to as 'Gwangcheon Terminal.'
Buses to Gurye depart almost half-hourly, but a few of them extend directly to Hwaeomsa Temple via Gurye. These particular buses are at 08:20 10:45 12:30 13:30 16:35 respectively.
Next leg from Hwaeomsa to Gongju or Buyeo is trickier no matter which city you decide to transfer through, there simply isn't a smooth connection. You could come out to Namwon (north of Gurye) first, where you catch direct bus to Dong-Daejeon (=Daejeon Dongbu). Not so frequent, 06:40 08:05 09:40 10:40 12:40 13:40 15:40 17:20 with possible minor adjustments.
Once you arrive at Dong-Daejeon, it is NOT necessary for you to travel across the city, since there are buses to Gongju from the same terminal you just got off, departing in every 40-ish minutes.

Thanks guys, makes my travel plans more concrete. Any advice about staying in the Jirisan Hwaeomsa area ? Or should I go to Gurye for more/better options ?