The town is very nice to explore on foot. Some cool old Soviet architecture, from the old hotels to the chess house are quite cool. Many old homes are of a very nice traditional style, and the river is quite good aside from the litter. There is even a sculpture park, an old ferris wheel needing repairs, and a semi-abandoned botanic garden. Aside from just exploring a bit on foot, there isn't much in the way of specific sites. It's just a pleasant town with some good places to explore in the region.
Makaravank Monastery
The biggest monastery near Ijevan if you count Goshavank as part of Dilijan's turf, this purple and green stone complex in the forest above the village is a popular spot for a picnic.
Yenokavan Canyon
This canyon is a like a time machine, where once you're past the top of the village, traces of modern life disappear. You are left with beautiful cliffs, forests, rivers, cascades, caves with deep carvings resembling Mayan or Aztec work, and a small camping area with a tree-house, a tiki-style bar, and other shelter made from the sticks and logs of the canyon. It's an awesome place where a guide will take you in, and set up your camping and food for you. Just call!
Srveghi Monastery
This red brick monastery is covered in the Shamshadin section surrounding Berd, but it's quite close to Ijevan.
Acharkut and Kirants Valley
Above these villages, following the mud road through the lush forest along the river, you first come to the turnoff to Arakelots Monastery on your right, then to the bridge on to your left to get to Deghdznuti Monastery, then further past the bridge is Kirants Monastery. All three are well worth a visit, and combined it's an awesome day... if you can find them!
Voskepar Church
This 7th century Armenian church in the ruined Azeri village of Askipari, is technically in Azerbaijan. Armenia now controls the territory now and the church is easily seen from the new highway, which is wholly in Armenia.
Misc. Churches around Ijevan
Some smaller and less significant/impressive churches in the area include the village churches of Gandzakar and Yenokavan, the smaller monastery or Moro-Dzoro near Lusahovit, and Ijevan's own smaller new church.