Usually, it's warm at noon time, and might be a little chilly in the mornings and evenings.
You can also expect rain (a 10-20 minute rain episodes, that may or may not appear, no worries).
After this "winter" we had, I really don't know. The above is how I remember the weather in March.
From Tel Aviv you can get almost anywhere in the country in less than 2 hours, except the very south.
I always recommend Jerusalem and Jaffa (:
If you'll be in Israel on March the 16th- it's a holiday, Purim - fun in Tel Aviv.
I hope something in all of this gabble was useful .