Beth, it takes me about 15 minutes from Syntagma to Hotel Phaedra, I think... I don't keep track of time when I'm busy enjoying the view. And maybe shorter at night since there's not as much to look at.
Here's the deal with pick-pocketing - based on my 12 trips (which have involved at least 20 stays in Athens). As far as I know, any pickpocketing instances reported on forums have involved only 3 locations... the Metro to/from the airport, the Metro to/from the port (both locations when people will be toting all their luggage & valuables), and in front of the Presidential palace during Changing of the Guards (the only time a crowd gathers & and people are distracted by the goings-on). I've never heard of someone rushing up on the street and snatching a purse or backpack off a tourist's shoulder (as has happened in Naples & some other major Italian cities).
As for security in Greece, here's been my no-worries procedure, once & for all (& I'm going to copy it for re-use on this constant question):
• IN TRANSIT - When coming into Greece, OR in transit to/from Athens on Metro, to get to ferry or plane & travel on those, when i've got everything with me. I have passport/cash/cc's etc in a Neck Pouch (I hate money belts because what woman needs MORE bulk around the waist!!!). I have change-purse & relevant ticket in a pocket zipped on inside of my SportSac daybag/purse, which I wear crosswise. Men can do neckpouch or moneybelt depending on how vain they are about their waistlines. Incidentally, I read that about 70% of Metro pickpocket reports involve pockets of men who swore 'I'd know if someone put their hand in my pocket."
• OTHERWISE - I stay in small family-run hotels, where cleaning staff is usually a niece or an auntie of the owner. I keep all that vital stuff in a concealed pocket in my big suitcase, which I lock. Have NEVER had any indication of anyone touch any of my things, in the more than 60+ hotel stays I've had. Walking around during the day, either in Athens or other mainland location or island, I do NOT carry my passport. NO need. Nervous Nellies can carry photocopies of 1st 2 pages if they wish. On nontravel days I carry in my pocket a small zipper-top nylon change purse, with the €€ I'd need for the day (+ my ATM card if I'm doing a withdrawal, or a Visa card if I'm making a CC purchase). Since it's fabric, it has a safety pin which I can attach inside my slacks pocket -- NOT to foil pickpockets, but because once when seated on an island bus, my change-purse fell out unnoticed ... fortunately, because of above policy, I was just out €15 & the cost of a new change-purse.
• PRECAUTIONS - I can be carefree because I'm A "belt PLUS suspenders" prudent person beforehand. I always have in my luggage • photocopy of 1st 2 pp of Passport • Contact info & account #s of all bank & credit cards •photocopies of reservation arrangements & confirmations • copy of travel med. insurance •emergency contact #s Of course I know that most of this info now can be stored on one's smart-phone... but on next trip I still will keep the "hard copy" because -- who has not had their phone battery die at an inopportune moment? Belt + suspenders = carefree traveler.