Hey, I have just done Everest base camp and did Annapurna base camp around 18 months ago. In all honesty, you would be better waiting until march if you want to miss the cold weather, but it does mean that there will be a lot more people. Everest, Annapurna and langtang are all well travelled, so have good facilities and western food.
Next time I go I will be looking at a more rural area as I like to get out and see the culture, something you miss on the base camp treks.
It will also depend what you want from the trek. Everyone knows Everest if you want bragging rights, but Annapurna was far more beautiful in my opinion.
If itinerary allows do spend sometime to explore Kathmandu and its temples. I could spend a week or more doing that alone.
Another vote for Annapurna and Langtang
Check who you travel with internally. Planes (the internal flight ones) are frequently overloaded, which was significant in the death of a friend last year but buses are not necessarily safer. Still life is not without its risks. A reliable company is what I would choose and I would tend to use bus rather than plane (which is technically quicker but prone to delays due to weather. The mad dash across the runway can be quite exciting though)
I would recommend restaurants etc. but they are probably all gone by now.
I recently posted a movie of exploring the greater Everest region in December last year that shows loads of places and things you can do and see on your own about the area. Note crampons/axe were useful at that time of year, despite the normal advice: