I’d love any suggestions!
I named my younger son [name]Asa[/name], which I love.
I also liked:
[name]Eben[/name]
[name]Avi[/name]
[name]Judah[/name]/[name]Micah[/name] (much more common, but not quite, like [name]Eli[/name]/[name]Ethan[/name] level)
[name]Sam[/name] (less popular than you might think, although I think [name]Samuel[/name] is kind of popular)
[name]Coen[/name]/[name]Cohen[/name] is kind of cool, and follows that whole [name]Jackson[/name], [name]Caden[/name] etc trend without being trendy at all.
[name]Abram[/name]
[name]Amos[/name]
[name]Esai[/name] (can you tell I like vowel-beginning names?)
[name]Asa[/name] was perfect for us, because I like Puritan names and my husband is Jewish. I think [name]Asher[/name] is slightly trendier, but still unusual enough.
[name]Ezra[/name], [name]Ephraim[/name], [name]Solomon[/name] come to mind. I also like [name]Judah[/name] and [name]Ben[/name].
My daughter would have been [name]Lev[/name] if she were a boy. I also like [name]Ira[/name]. I like the shorter names I guess.
I absolutely love [name]Avram[/name], [name]Ariel[/name], [name]Mordecai[/name], [name]Lior[/name], and [name]Dov[/name].
I like [name]Zev[/name], [name]Ilan[/name], [name]Jeb[/name] and [name]Ephraim[/name].
I am really in love with the name [name]Boaz[/name].
I’m loving:
[name]Jethro[/name]
[name]Abner[/name]
[name]Reuben[/name]
[name]Solomon[/name]
[name]Jude[/name]
[name]Abel[/name]
I like [name]Zev[/name] -it means wolf. I would avoid the suggestion of [name]Cohen[/name]/ [name]Coen[/name] as it’s a pretty controversial trend.
We’re Jewish and considering [name]Jonah[/name], [name]Zev[/name], [name]Benjamin[/name] and [name]Ezra[/name] for a boy - not all modern or unusual but each one fits our criteria of being Hebrew AND having a family/personal significance.
Ditto not choosing [name]Cohen[/name]…
As far as modern goes…I love [name]Ezra[/name] and we almost used it as a first name but its one of our ds’s middles. Also, [name]Levi[/name] (used as a middle), [name]Seth[/name], [name]Micah[/name] (too similar to [name]Mike[/name]/[name]Michael[/name] for my personal taste but its a neat name), [name]Jonah[/name] (very popular where I live but I love the sound of it), [name]Ari[/name], [name]Judah[/name], [name]Gideon[/name], [name]Reuben[/name], [name]Isaac[/name]…brain freeze thinking of more.
Unusual, well, again, we chose [name]Elihu[/name]. Helps that I’m a Phish head so it doubles for anybody in that crowd. 
Also [name]Lemuel[/name] but since I read the [name]Red[/name] Tent I cannot get over the “character” of [name]Lemuel[/name].
I’ve wondered about that when I’ve seen your signature 
I always sing “Dancin’ with [name]Elihu[/name], up on Leemor’s bed” when I read it. I can’t say I am a current Phish head, but spent a significant part of my college years and a bit beyond with the Phish head crowd and going to shows. My SO is still a HUGE Phish head.
I really like the name [name]Ari[/name].
Not Jewish, but I really like [name]Yael[/name] and [name]Boaz[/name]. [name]Elijah[/name] is an all time fave for me also.
I like:
[name]Noam[/name], [name]Ari[/name], [name]Zev[/name], Tzvi, [name]Gilad[/name], [name]Aryeh[/name] for Jewish but not strongly Biblical.
and
[name]Gideon[/name], [name]Naphtali[/name], [name]Ephraim[/name], [name]Ezra[/name], [name]Mordecai[/name], [name]Malachi[/name], [name]Phineas[/name], [name]Zebulon[/name], [name]Hezekiah[/name], [name]Azaria[/name] - the semi-quirky Biblical names I like.
Actually I don’t know if you’d count [name]Aharon[/name] or [name]Reuven[/name], etc. as uncommon or not. [name]Aaron[/name] and [name]Reuben[/name] are mainstream, but are those? [name]Zevulun[/name] probably didn’t get much weirder than [name]Zebulon[/name] is anyway. I’m fond of [name]Gavriel[/name].
[name]Jethro[/name] I’ve heard called hickster, Yitro is definitely uncommon, I like both.
[name]Meir[/name] (pronounced like [name]Meyer[/name])
I know a 3 year old [name]Meir[/name] and he’s the cutest thing!
Also not Jewish, but I cannot get over [name]Avi[/name]. I’ve loved it for a long long time.
I’ll third the notion not to use [name]Cohen[/name].
On my list when I was pregnant: [name]Judah[/name], [name]Benjamin[/name], [name]Ariel[/name], [name]Azariah[/name], [name]Micah[/name], and [name]Jonah[/name]. I have friends who have sons named [name]Eli[/name], [name]Rafael[/name], [name]Lev[/name], and [name]Yossi[/name].
Good luck!
[name]Susan[/name]
Some more modern Israeli names you will hear there
[name]Ziv[/name]
[name]Gil[/name]
Matan (means gift or present)
[name]Dov[/name] (means bear)
[name]Doron[/name]
[name]Aviv[/name] (means spring)
Yuval
Shaked
Ronen
Tomer
Those are all great choices. We are also Jewish and considering [name]Jonah[/name], [name]Lev[/name], [name]Liev[/name] (Yiddish), Matan, [name]Omri[/name], [name]Noam[/name], Etrog and Lulav. I am just kidding about the last two - that’s my DH’s bad joke 
Right now, [name]Jonah[/name] is our #1, despite the fact that it reminds me of the little boy from Sleepless in Seattle!
I loved the name [name]Asher[/name] for years but now all of a sudden it’s heading for the top 50, so we dumped that one. I also love the names [name]Avi[/name] and [name]Aviv[/name], but I grew up with two of them, so the names are ruined for me (to use) due to the strong connotations. I also have family in [name]Israel[/name], so the following names are out for me, but might work for you: [name]Micah[/name], Aviad, Yoni, [name]Nati[/name], [name]Natan[/name], [name]Eitan[/name], [name]Dan[/name] (pronounced DahhN), [name]Shlomi[/name], [name]Guy[/name] and [name]Ari[/name]. We had briefly considered [name]Zev[/name], but the more common name/spelling in Hebrew is actually Ze’ev. I don’t want any pronunciation issues, so we will probably dump [name]Liev[/name] for the same reason. And I third (fourth?) the rec of not using [name]Cohen[/name] as a first name, not because it’s trendy, but because if you or your husband are not in that tribe, it’s kind of a misnomer.
Good luck - would love to hear what you end up going with!