The Sword Coast area is huge, and there have been dozens of novels set there over the years. Very few of those novels are primarily set specifically in the small chunk of it covered in
Lost Mine of Phandelver and
Dragon of Icespire Peak. I'm going to assume that's the area you're primarily focused on.
On the merits, the best novel set in and around (but mostly in) Neverwinter is Erin Evans's
Brimstone Angels. Good luck finding a print copy for less than $100. Print runs for D&D novels in the 4th-edition era were at an all-time low, and since the player base has ballooned in the past ten years, copies of novels from that era can now be very pricey. The ebook is of course still reasonably priced.
Another good choice might be
Thornhold by Elaine Cunningham. This is billed as book 4 of the "Songs and Swords" series, but don't let that fool you: it's a standalone novel that requires no prior knowledge and doesn't really relate to the books before and after it in the series (it was in fact written as an installment in the loosely connected, long-running "Harpers" series, but WotC pulled the plug on the Harpers books and reassigned the novel to "Songs and Swords").
Thornhold is set partly in Waterdeep but also in key locations located just off the map included in the Essentials Kit (to the south and west), including both the titular fortress (at the southern edge of the Mere of Dead Men) and also some locations in the Sumber Hills; this would be a good way of getting the group excited about exploring the wider world without traveling too far, if that's something that interests you. A key subplot of
Princes of the Apocalypse uses characters, locations, and lore from this novel.
Option 3 would be the "Icewind Dale trilogy":
The Crystal Shard,
Streams of Silver, and
The Halfling's Gem. These were the first three novels published starring the now-famous drow ranger Drizzt. (Watch out, the "Dark Elf" prequel trilogy that starts with
Homeland is often listed as the "first" Drizzt trilogy but is not the one you want.) The writing in these is simpler, perhaps well suited to the age group you mention; the style is not my favorite, but it
is a lot of readers' favorite. In
Lost Mine of Phandelver the party can encounter an NPC (Agatha the banshee) and visit locations (her lair and the village of Conyberry) that originate in the third novel of this trilogy.
One other thing to mention, I guess, is that most of the D&D novels TSR and WotC published over the years were written for an adult readership. Some of them include scenes of sex and violence (and sometimes even sexual violence) that would never in a million years receive the stamp of approval from WotC today, because "the culture" has shifted a lot regarding such content since then and the D&D player base skews younger on average now than it used to. (WotC used to target twenty- to thirty-year-old players and worked hard to fight against the conception that D&D was a game for middle- and high-school kids; now they actively pursue and arguably prioritize players in that age range.) I don't recall anything potentially objectionable in the novels I've recommended—but when I read them, I wasn't actively screening for such content, so I can't be sure (except about the Drizzt books, which I think are definitely age-appropriate). I'd recommend that you read any novel you want to give to kids in that age group first yourself—which shouldn't be too great a hardship, since these are fun books!
As for
Dragons of Stormwreck Isle, I don't think anyone outside of WotC and its playtest groups knows for sure what's in it. All we know is:
- Its table of contents appears (in a blurry but mostly legible promotional image) to have a section titled "The Forgotten Realms," so it's almost certainly an FR adventure.
- If it is an FR adventure, it's probably set on the Sword Coast (or, given the title, on an island in the Trackless Sea off that coast), because that's where WotC has set the vast majority of the 5e FR adventures.
- There is no location called Stormwreck Isle in established FR lore.
