One way to look at "elvish" features is to compare how different elvish languages look, and to take inspiration from that.
A look at the phonologies of a few elvish languages:
Quenya
(phonology from here)
Labial Alveolar Palatal Velar Glottal
Nasal m n ŋ
Stop p b t d k g
Fricative f v s (ç) x h
Trill r
Semivowel (ʍ) w j
Liquid l
Front Central Back
Close i(ː) u(ː)
C-Mid eː o:
O-Mid ɛ ɔ
Open a(ː)
Sindarin
(phonology from here)
Labial Dental Alveolar Lateral Palatal Velar Uvular Glottal
Nasal m n ŋ
Stop p b t d k g
Fricative f v θ ð s ɬ χ h
Trill r
Approximant l j ʍ w
Front Central Back
Close i y u
Near-C ɪ ʊ
O-Mid ɛ ɔ
Open a
Some common denominators in Tolkien's Elvish: They all have distinction between voiced and unvoiced stops and (labial) fricatives, both have the somewhat /ʍ/ as a phoneme or allophone as well as /ŋ/, /x~χ/ and /h/. With vowels, they each have four vowel heights but nothing much in common beyond that. Allowed syllables seem to be (CC)V(CC) in Quenya (many more details at Wikipedia) and (C)V(C) in Sindarin, though I don't see that explicitly.
Pathfinder Elf Names
(names from here)
Male Names: Caladrel, Heldalel, Lanliss, Meirdrarel, Seldlon, Talathel, Variel, Zordlon.
Female Names: Amrunelara, Dardlara, Faunra, Jathal, Merisiel, Oparal, Soumral, Tessara, Yalandlara.
My interpretation of the names hints at some of these features: Only two nasals, voicing distinction, five vowels.
Allowed syllables: Apparently (C)V(CC) or (C)V(LC) where L is a liquid (l or r) or nasal
Dungeons & Dragons Elf Names
(names from 3.5 edition Player's Handbook p. 16)
Male Names: Aramil, Aust, Enialis, Heian, Himo, Ivellios, Laucian, Quarion, Soveliss, Thamior, Tharivol
Female Names: Anastrianna, Antinua, Drusilia, Felosial, Ielenia, Lia, Mialee, Qilathe, Silaqui, Vadanja, Valanthe, Xanaphia
Family Names: Amastacia, Amakiir, Galanodel, Holimion, Liadon, Meliamne, Naïlo, Siannodel, Ilphukiir, Xiloscient
Here we seem to have gemination at the end of words, vowel length, maybe uvular stop; th and ph are probably fricatives and not aspirated, judging by the presence of v and absence of f. Syllables seem to be (C)V(CC).
Using the very questionable methodology of taking the least common denominators of all of them would give us something like:
Labial Dental Alveolar Palatal Velar Glottal
Nasal m n
Stop p b t d k g
Fricative f v θ s z h
Trill r
Approximant l j w
Front Central Back
Close i u
Mid e o
Open a
If you want an elvish language to be easily recognizable as elvish, you might be able to copy some of these features. I'm not sure, though, that there is any feature that might be universally understood as elf-like.