Does an opponent get priority between you playing a land and tapping it for mana?

Playing a land is a special action defined in CR 116.2b. Special actions do not use the stack and do not cause players to receive priority afterward in the same way spells and abilities do. After you take a special action, you simply retain priority (CR 116.2b, 117.3b).

Because you keep priority immediately after playing your land, you can tap it for mana right away by activating its mana ability. Mana abilities themselves also don't use the stack and don't allow opponents to respond (CR 605.3b). This means the sequence of playing a land and tapping it for mana is effectively uninterruptible by opponents.

This matters most when you need that mana urgently — for example, to cast a spell during your main phase. Your opponent cannot "respond" to your land entering the battlefield to destroy it before you tap it for mana, because you never pass priority between playing the land and activating its mana ability.

Concrete example: You play a Forest. Before passing priority, you immediately tap it to produce one green mana. Your opponent wanted to cast Strip Mine's effect at that moment, but they never received priority, so they cannot destroy the Forest before you generate the mana.

Note: Opponents can respond to spells or non-mana abilities you cast/activate using that mana, since those go on the stack — but they cannot stop you from producing the mana itself after playing the land.