The suburbs of Kaunas are unique for having a separate Lithuanian word to describe them all: Pakaunė.
The Pakaunė village that sees the most foreigners is undoubtedly Karmėlava where Kaunas airport is located. It has little to offer but is famous for its Cepelinai, the traditional Lithuanian meal is provided here far bigger than usual. Look for signs "Hyper Cepelinai", "Cepelinai XXXL" and similar in the village. The taste of such giants may differ from the true deal somewhat but this fails to discourage Lithuanian emigrants on short visits back who gouge the oversized versions of the meal that is, effectively, *the* symbol of Lithuanian cuisine.
The population of Pakaunė is growing even though the city itself plummets. People leave the city for private homes there: large self-designed mansions in the 1990s and more modest yet elaborate today. Many of the new residential suburbs replace old "collective gardens", a uniquely Soviet program of allocating urban dwellers some suburban land to farm and spend summers at.
The most unique place there is AB spaustuvė, an illegal printing house for censorship-free materials under the Soviet occupation. Vytautas Andziulis built it slowly and secretly under his garden greenhouse and managed to operate undetected from 1980 until 1990 independence, printing 138 000 books with his Spartan machinery (assembled underground using the parts government discharged). The place now operates as a museum that unites well-hidden original "printing dungeon", pre-PC era printing machinery, Andziulis's symbolic art and the heroic-yet-tragic stories of Lithuanians who defied the occupational censorships they endured (Russian Imperial, Nazi German and Soviet). Ab spaustuvė also gives you a glimpse of Pakaunė with a large Andziulis's home which housed his unsuccessful legal printing business in the 1990s (like many early trial-and-error entrepreneurs Andziulis was outcompeted by modern machinery). Pre-arranging the visit at the War Museum may be necessary.
Raudondvaris suburb west of Kaunas is famous for its "castle", actually a 17th-19th-century manor that has been built to look like one. This is the first of the Castles of Panemunė.
On the southern bank of Nemunas the Zapyškis village is famous for its unusual small gothic church (~14th-16th centuries). No longer used for religion since a new church has been built uphill (1942) it is now an atmospheric venue for sporadic summer concerts hailed for great acoustics.
Some famous places are located near the outskirts of Kaunas but are parts of the city-proper or described as such for clarity: the 9th fort of the Kaunas fortress, Pažaislis monastery and the neighboring Kaunas Reservoir.