Nero waited 25 years then intercepted Spock, captured him, and marooned him on Delta Vega. But Spock settled within walking distance of a Federation science lab (where Scottie ended up). He brought young James T. Kirk there to get beamed back to the Enterprise. Why didn't he just take a short walk over there sooner and perhaps ask to make a phone call about Nero and what he may be planning, ask for transport to Vulcan or Earth, etc?
This answer involves a speculative leap.
After landing on the planet, the escape pod informs Kirk of the location of the outpost:
COMPUTER VOICE: Location: Delta Vega. Class-M planet. Unsafe. There is a Starfleet outpost fourteen kilometers to the northwest.
Kirk has been walking towards that outpost when, chased by the local fauna, he stumbles into a cave and is saved by Ambassador Spock, who then initiates a mind meld:
KIRK: Whoah, whoah. What are you doin'?
SPOCK PRIME: Our minds. One and together.
And, following the mind meld, Ambassador Spock whips out his knowledge of the base:
SPOCK PRIME: Jim, we must go. There is a Starfleet outpost not far from here.
We could speculate that Spock learned of the Starfleet outpost by mining that detail from Kirk's mind when they were "one and together"; Kirk, of course, knowing about it from the escape pod computer. If Spock was not aware of the base before the mind meld - or knew, from his timeline, that such a base existed, but not where he was relative to it - then that would explain why he hadn't gone there before the meeting with Kirk.
There are many explanations possible here. The fine details are simply not part of the movie.
How do you know Spock hadn't already been traveling towards that outpost? For all you know, he was taking a break when Kirk showed up. We don't know where Nero dropped Spock off. He may have been stranded considerably further than Kirk, since Kirk was launched by a Starfleet vessel with the express intent to be picked up by Starfleet personnel from the outpost. Spock, on the other hand, was dropped somewhere he could watch Vulcan.
Spock's homeworld was just destroyed, and this Spock wasn't even aware that anyone was rescued. It's not beyond the realm of possibility that he wanted some alone time.
Spock may have been sheltering from the cold. He had a fire going, and we do not know how long him and Kirk spent in that cave before actually moving on. Given the low visibility when Kirk didn't spot the approaching creature, the weather wasn't being particularly hospitable.
Gowenfawr and jeffronicus' suggestions are possible too. Though I'd expect either case to be explicitly mentioned given that they'd be an interesting addition to the script.
Why didn't he just take a short walk over there sooner and perhaps ask to make a phone call about Nero and what he may be planning, ask for transport to Vulcan or Earth, etc
- Spock doesn't know Nero's plan. Nero didn't even know Nero's plan after punishing Spock.
- Vulcan was already destroyed at this point, and both Spocks were made painfully aware of that fact.
- Before the destruction of Vulcan, Starfleet's fleet had been destroyed. Spock likely witnessed this, as he was already on the planet, Nero was already drilling Vulcan, and the fleet must have engaged Nero in plain sight of Spock. The appearance of the Starfleet fleet means that Starfleet is already aware of Nero's presence. Spock doesn't need to inform them about it.
- Also note that Vulcan, as a Federation member, would be in contact with Starfleet as well, even before Nero started drilling. This is presumably how Starfleet was initially made aware of Nero's presence to begin with.