Have a look at my Savegame

Not on a computer with civ right now, but why exactly is having a vassal bad? Sounds like you did something right if people want you to be their master...
 
Eh, I always see them as a good thing unless they are at war with someone you really like when they want to become your vassal. You can essentially be as mean as you want to them and deny them anything because they have to listen to you. They can't declare war on you, and I usually actually demand things from them. You also get 50% of their land and pop for victory.
 
A few very quick pointers;

(1.) Review your civics!

(2.) {I can't believe I'm saying this, but} you might want to look at building some Wonders in light of your Marble (and Ivory for the Statue of Zeus if that's of interest). Wonder addiction can be a problem, but having The Great Library as an option on your build queue when you have no combat pressure whatsoever and access to Marble - seems too good to ignore. The Parthenon and The Mausoleum of Maussollos both have their uses. Even though you don't currently have Stone, the Maoi Statues is a handy National Wonder given several of your coastal cities are well developed.

(3.) While you're Financial, I wouldn't completely discount running a few Specialist Scientists with the view to popping a few Great Scientists - an Academy in your capital is usually a strong play.

(4.) Send out an exploration boat - you might bump into other civs and get some catch up deals going - aim to trade the same tech' to multiple leaders for a 2-for-1 or 3-for-2 type round of negotiations if at all possible.
 
Ya the biggest thing that stands out to me is your civics. Why in the world aren't you running Bureaucracy? Organized Religion wouldn't be a bad idea either.

Normally I would say your military is rather lacking as well, but seeing as how your only rival is a willing vassal, at this stage it's not as important. It might be tho once you meet more civs.

Actually what I would do is grab machinery, pump out macemen, wipe the Egyptians out and monopolize that continent, but that's just me. They're really not helping you much as a vassal, they don't have tech parity with you so you can't toss techs off each other, and all that land, production and commerce would better serve you under your direct control.
 
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