Well, it's a giant field full of people picknicking and many do bring kids (as youngsters get free admission, I think). So they will be around. But that being said, it's still a venue that I really enjoy and I think you will, too. It's a chance to sit in a lovely field.
If being up close is important to you, getting there the earlier the better is helpful. Yes, members get early admittance, but there is still lots of room after they're seated. As with all field concert seating (The Gorge, Bumbershoot, etc) you can generally weave your way through the crowds and find a space to sit between already seated folks, ya know? Especially as you are just a solo person, this should be easier. While I don't think bringing a chair is necessary, I think you will be MUCH more comfortable if you bring a blanket to sit upon, and maybe a pillow to help cushion your seat...as you really are just sitting on the ground. Also, bringing a blanket will help you CLAIM YOUR SPACE. Others will respect the boundaries of your blanket, but if it's just you sitting on the ground, other groups may end up squeezing right up next to you. So stake your claim with some fabric. *smile* AND, your later seating should allow you to better scope out potential neighbors.
While there tend to be lots of children around, I've found that everyone is generally respectful and quiets their conversations once the acts begin (not always true for the opening act, but for the main performer, people tend to quiet down). We've asked, politely, once or twice, for our neighbors to curtail their chatting, and they've always complied.
We tend to sit towards the back, and in my observations, it's seemed that families with kids tend to sit towards the front and the sides (that way folks send their kids to run around on the edges of the crowd)...so maybe the front-center will give you a better seat with less likelihood of frolicking nearby. Honestly, the field isn't that large, so even sitting towards the back you're not too far from the stage.
I respect that you're not really interested in the picnic/drinking scene, but I'd encourage you to at least pack some snacks, if not your dinner. Sometimes other people eating bothers me (MOUTH NOISES!!) but if I'm chewing on my own food, it doesn't irk me so much. So maybe some trail mix or something? *shrug*
I think you'll have fun. Lucinda should be great (I'm going too!!). It's a pretty casual venue, and it's family friendly. The volume levels are not AS high as other concerts, because zoo staff are trying to strike a balance between the concerts and animal discomfort.
Also, IF you are interested in chatting with strangers, it's the type of event where people often will talk to their blanket-neighbors. But it's also Seattle, so folks should totally leave you alone, if you prefer.
Good luck! There will be some vendor booths around the field with free samples, information, and then some food options, too, if you'd like to purchase something (your blanket also helps here, to save your spot while you can wander around). And, worst case, if you end up with crappy concert neighbors, you can generally move without too much trouble (once we were next to some 40-somethings HEAVILY drinking the wine and talking loudly who were crazy rude, so we just picked up our blanket and found a new place to sit).