With increasing social mobility and an aging society, more older adults in China are migrating to new cities, known as "older drifters." Due to fewer social connections and cultural adaptation challenges, they face negative emotions such as loneliness and depression. While reminiscence-based interventions have been used to improve older adults' psychological well-being, challenges such as the lack of tangible materials and limited social resources constrain the feasibility of traditional reminiscence approaches for older drifters. To address this challenge, we designed RemiHaven, a personalized reminiscence support tool based on a two-phase formative study. It integrates "In-Town" and "Out-of-Town" peer agents to enhance personalization, engagement, and emotional resonance in the reminiscence process, powered by Multimodal Large Language Models (MLLMs). Our evaluations show RemiHaven's strengths in supporting reminiscence while identifying potential challenges. We conclude by offering insights for the future design of reminiscence support tools for older migrants.