If you can find it, "Necropolis," written by Gary Gygax and published by Necromancer Games for d20 has tons of inspiration for an Egyptian civilization. It also has some pretty lethal dungeons that hearken back to Tomb of Horrors in many ways. Great stuff.
For inspiration on a fantasy Greece, I would look to some of the lore from the MtG Theros set. It had some really good city-state ideas and a good spin on the Greek gods. There is also an OSR game called Mazes and Minotaurs that I think you can get for free.
Ran session 1 today, Tomb of Tiberish was a bit rough as we had not played for a bit and 2/4 PCs were doing some odd things sometimes. Next session we should have 5 so an extra PC should help alot. Huge difference at low level in regards to having a life cleric/healer feat vs not having one.
Gnolls are very dangerous at level 2 one encounter was 3 of them + pack lord. We had rolled stats and I think most of them managed to get an 18 after racials and/or various +1 feats (I allowed a bonus feat lvl 1 to make up for inferior equipment).
Thinking of a bit of satire like claims the pyramids were built by godlike being from beyond the moons. Might even put a ruined spelljammer ship in a tomb. Mummified dragons are another possibility and I invented a few languages to tie the PCs to the game and so they could take some relevant languages as part of that.
Level 3 thinking of RP/hexcrawl mapping out upper Nithia or an urban adventure. While they are low level an environment adventure might be better IMHO as its harder to pull off later on.
Just want to throw this out there: the "fancy names" we Westerners see on many foreign cities have literal name meanings. "City of the Sun", or "City of God" or "City on the River" or "City of Famous Person" are common ones in many cultures. Don't go overboard trying to make up names of cities and towns. It turns out people name their cities and towns pretty much the same regardless of the language.
Something that may be of interest to the posters here is the "first city" setting presented in "the Peridot" - it's essentially one of the first city ever, at the very dawn of civilization. It's done as a hexcrawl, and is very OSR in feel: