If my opponent wins combat at a battlefield and I have 2 units, and a Zhonyas in my base, can I choose who the Zhonya saves?

Yes, you can choose which unit to save.

According to RiftJudge FAQ #6895 and FAQ #1042, when multiple units die simultaneously from combat damage, the controller of the Zhonya's Hourglass replacement effect chooses which unit's death is replaced.

The Breakdown:

1. Simultaneous Deaths: Although combat damage is assigned in an order, it is dealt simultaneously. Therefore, if both of your units are dealt lethal damage, they both enter the "dying" state at the exact same time during the Combat Cleanup step.
2. Controller's Choice: Because you control the replacement effect of Zhonya's Hourglass, you decide which one of those simultaneous death events to replace (Rule 373).
3. Location Independence: You mentioned having the Zhonya's in your base. Location is irrelevant for this interaction. Whether your Zhonya's Hourglass is hidden at a battlefield or already in your base, it functions as a replacement effect that triggers when a friendly unit would die. As stated in RiftJudge FAQ #1042: "Location is irrelevant - if a unit dies at any location, you can use Zhonya's to save a unit anywhere."
4. Requirement: You must have the Zhonya's Hourglass face-up on the board before the damage is dealt to have it active, as it is a replacement effect and not a triggered ability (RiftJudge FAQ #8618).

Sequence Summary:

• Combat Damage Step: Combat damage is dealt to your units.
• Death Event: Both units would die simultaneously.
• Replacement: You apply the Zhonya's Hourglass replacement effect to one unit, which saves it (heals it, exhausts it, and recalls it to base).
• Result: The chosen unit is saved; the other unit proceeds to die as normal.

This is my interpretation based on the mechanics of replacement effects and simultaneous death events as outlined in the game rules and verified by the cited FAQs.