Thanks to everyone for all the helpful replies. Sounds like I have two good options for a full day hike: (1) Up Ammo and down Jewell, or (2) Up Lions Head and down Tuck. I'll definitely need to check the posts in mid-May and then decide. A couple of follow-up questions...
If I do (1), what is the likelihood that there will be snow on the Ammo and Jewell trails in mid-June? Do I need spikes/snow gear? I know it's been a snowy winter, but since I've never been there I don't have a good feel for what the conditions will be on the various trails. I assume if I did this trail it would be best to use the AMC Highland Center as my base (my current reservation is at Joe Dodge/Pinkham Notch).
If I do (2), I assume sections of the Tuck trail will be off-limits due to avalanche issues. Does this typically affect the entire trail (as well as Lions Head), or just sections of Tuck? Can I still fit in a hike along the Alpine Garden Trail, which I hear is beautiful in June?
Thanks again everyone!!