Bereishis Rabbah 19:3:
וְהֵיכָן הָיָה אָדָם בְּאוֹתָהּ שָׁעָה, אַבָּא בַּר קוֹרְיָיה אָמַר נִתְעַסֵּק בְּדֶרֶךְ אֶרֶץ וְיָשַׁן לוֹ. רַבָּנָן אַמְרֵי נְטָלוֹ הַקָּדוֹשׁ בָּרוּךְ הוּא וְהֶחֱזִירוֹ בְּכָל הָעוֹלָם כֻּלּוֹ, אָמַר לוֹ כָּאן בֵּית נֶטַע, כָּאן בֵּית זֶרַע, הֲדָא הוּא דִכְתִיב (ירמיה ב, ו): בְּאֶרֶץ לֹא עָבַר בָּהּ אִישׁ וְלֹא יָשַׁב אָדָם שָׁם, לֹא יָשַׁב אָדָם הָרִאשׁוֹן שָׁם.
So either Adam was sleeping after having had relations with Chava, or Hashem had sent him on a world tour to identify the various types of agricultural lands.
A couple of the assumptions in the OP are also questionable:
"Eden doesn't seem to be a huge place to walk around": (1) they were actually in the Garden, not in Eden itself. Those aren't the same - "a river flows out of Eden to water the Garden" (Bereishis 2:10), and Chazal point out that no human eye has ever seen Eden (Berachos 34b, Sanhedrin 99a). (2) Chazal also state (Pesachim 94a, Taanis 10a) that the entire world is 1/60 of the Garden, which in turn is 1/60 of Eden. True that such expressions aren't necessarily literal, it would still mean that the Garden (let alone Eden) is pretty big.
"Adam and Chava didn't have anything important to do, after all, they weren't positively commanded on doing anything": what about לעבדה ולשמרה? Whether you take those in the literal sense, or as referring to mitzvos,* that's definitely something they were commanded to do.
* A number of early acharonim (Alshich, Shaloh, etc.) quote a maamar Chazal לעבדה אלו מצות עשה ולשמרה אלו מצות לא תעשה, though I haven't found the original source. In Bereishis Rabbah 16:5 it does bring one opinion that they refer to working during the six weekdays and keeping Shabbos, and another that they refer to the korbanos.