As it has been mentioned before, Kolonaki is to be visited, if one is looking for more upscale brands. The neighborhood is just above Syntagma (where your hotel, the Grande Bretagne is located). Now is the summer sales period here in Athens, and you can find discounts up to 50%, but you may encounter some difficulty finding something you like in your size.
Anyway, you should check out the Attica mall, it's just around the corner from your hotel, between Panepistimiou and Stadiou streets. Huge selection of brands. Also the stores in the basement and the gallery of the same building (Ferragamo, Hermes, etc)
Moving upwards from Syntagma, you should walk up Voukourestiou street, towards Kolonaki. Check out the shops along the way and on the sideways. Perhaps of interest to you is Green, at Voukourestiou and Skoufa. A rather american/ ivy league/ conservative east coast kind of place (wooden interior, leather furniture, etc), carrying Ralph Lauren, Allen Edmonds and the like. Walk Skoufa towards Kolonaki square, and when you find it, take a left in Patriarchou Ioakeim. Carouzos is to be found there (carries Zegna, Brioni, Kiton, Prada, Gucci, Santoni, Jil Sander etc - also bespoke shirt service with Zegna shirtings). Also, both in Panepistimiou and Patriarchou Ioakeim you can find Giannetos. It's the most established bespoke tailoring firm in Athens. They have their own RTW line, starting from 600 euros, and bespoke starts from 1200, and rising really fast. Especially the Kolonaki place (in Patriarchou Ioakeim) is the one to visit. Of course, there are other tailors, but I believe that is the only place where you can find someone that will be able to speak english and assist you.
Finally, below Skoufa, the parallel street is called Solonos. There is this store in the beginning of Solonos called Observatory. A nice place for casual dress, it carries Fred Perry, Penguin, Smedley, Rag & Bone jeans and the like.
Kolonaki is a more upscale place, long associated with the upper class, and hence the selection of brands there. But you should also check Aiolou street, below Syntagma square. Going down Ermou (the major commercial street of Athens) you'll find mostly shoe stores and high street brands (Marks & Spencers, Zara, Massimo Dutti etc). There you will find the Lacoste and Fred Perry stores. Especially the Fred Perry has everything 40% off, and it also has special prices on past season items. When you hit Aiolou, take a right. The place looks pretty decayed, but up until 40 years ago this is where the commercial and merchant centre of Athens used to be. Along the way you'll find the cloth merchants. The shops don't look like much, but they carry a good selection from various brands (Dormeuil, Zegna, etc), and decent discounts this time of the year. My opinion, if you have to buy only one thing, buy cloth.
Also check out the market district of Glyfada. Glyfada is one of the south suburbs, along the coastline. There is a Carouzos outlet there. Most of the items are 70% off retail, and sometimes even more.
As for going out, eating, etc, depends on your tastes. Definitely go for drinks on the roof bar of the Hilton, named Galaxy. Great cocktails and an amazing view. Gazi is the hottest place now downtown. It's the area near the old gas factory (great industrial architecture, nowadays used for art exhibitions, festivals, live concerts, etc). Also Psyrri is a neighborhood to visit for the night life. Lots of bars around the area. If you look for more mainstream clubbing, you should check one of the clubs at the waterfront of Athens. Not my scene though.
I really hope the above has been helpful. If you wish to ask anything more specific, don't hesitate to contact me.
I hope you enjoy your visit,