1) Stay in the Pacific and actually try to defend some place.
I think there were a host of reasons pointing to this being the best option. The plan being, to leave Leipzig and Dresden in the Americas raiding independently, to send Emden and Nurnberg into the Indian Ocean as raiders, and for Spee's armored cruisers accompanied by the Austria protected cruiser Kaiserin Elisabeth to venture south to defend German possessions. Advantages -
1. The Spee squadron, IIRC, mustered something about 15,000 or 18,000 tons of coal for the voyage to South America aboard a motely collection of available shipping. (I would have to double check). The distance from Marianas (the assembly point) to South America was enormous, at 8,300nm. With the exception of the Emden, all the assembled coaliers and warships basically expended several months and huge amounts of the coal reserve to pass through the vast wastes of the Pacific to reach Craddock's squadron. Logistically, keeping the armored cruisers inside the German Pacific Islands belts was much better. There were plenty of places to hide, and far more time could be spent not moving, letting that initial coal reserve go much further even after Emden and Nurnberg peeled off with 8,000 tons for their own adventures.
2. Spee's decision to remove himself from the scene and sail east allowed the British breathing time to organize their defenses. If Spee's squadron had stayed, and managed to pounce on some force or other, the movements of the Entente forces would have been less efficient, more confused.
3. Some of the infantry forces at Tsingtao, plus Spee's squadron's ammunition reserve apparently left behind, could have been sent south on the mustering coaliers, which was a better use of them since they could not be penned up later. If one of Spee's ships were damaged in battle, it's crew could more easily switch over to the infantry role, whereas going to South America basically took this option off the table.
4. Spee had one key advantage in the Caroline region early in the war - the German wireless network. Unlike in his blind fumbling around South America, in the region of Rabaul and Palau, Spee could wait at an anchorage for an opportunity to attack one of the Entente squadrons attacking various islands, using information on the enemy's strength and location broadcast by his wireless network to decide if and when to offer battle. (For example, wait at Ngulu Atoll or the islands around Kavieng). Spee was the spider, the wireless network his web. Nowhere else he could go would he have this advantage of the element of surprise and better intel.
Tactically, Spee's objective I think should have been to take a shot at the one thing that he and many others thought to be unthinkable - to find and sink the HMAS Australia. This would be worth both of the armored cruisers in his squadron. The 'how' for that was simple. To place infantry at Rabaul to bolster the garrison so that any Australian invasion would take at least a week. Then, when reports that Australia was anchored off Rabaul in support of the invasion, come around the south side of New Ireland and sail into Rabaul harbor in the middle of the night (Savo Island style) to engage Australia at anchor at point blank range with both armored cruisers. (German shore based forces could broadcast Australia's precise location using the inland wireless transmitter).
If Spee actually sank Australia, the balance of power in Australian waters would be transformed immediately, and Spee would have a window of maybe a month to dominate the waters off the Australian east coast and completely disrupt Australian war planning and troop movements by sea.