The current version of MapPress reads all the posts for the map, so that query dictates the memory usage/time.
I think WordPress itself (with no plugins) uses around 40MB, so 64MB doesn’t sound extraordinary.
If the problem is a memory limitation, you’ll need to increase your PHP memory or set a “posts_per_page” limit in the query. Here’s the codex entry:
Please note that most hosts require you to edit the php.ini file, so just setting WP_MEMORY_LIMIT in wp-config.php won’t always work.