I was offered a chance to buy a house earlier in the game but turned it down as I did not have enough gold. Now that I do - I can't find the person or remember the town that it was offered? Any help on this topic?

Whterun is the first and cheapest house you can buy. You need to talk to Proventius Aventius (or something close to that, not sure of the spelling). You'll find him inside Dragon's Reach in Whiterun usually standing near the Jarl or sitting at the long tables.

Sounds like Whiterun. Go to Dragonsreach and talk to the steward (normally standing next to the Jarl in daylight hours). He's the one with the house and furnishings.

Just remember; The steward in the castle, palace, or Keep is the one you talk to when you want to purchase a house in any of the 5 Hold's.

http://elderscrolls.wikia.com/wiki/Houses_%28Skyrim%29.

there are only 5 places to buy houses

whiterun
markath
solitude
riften
windhelm

go to each of these places, at the castle
and talk to the steward (not the jarl, the other guy usually sitting or standing close to the lord)
the option to buy a house should show

Also you will know based on quests you did

whiterun: main quest, kill the first dragon in game (if you killed any dragon, that s the one)
markath : clearup a big forsworn redoubt (red eagle redoubt, I think), then clear an hagraven nest
solitude: clear wolfskull cave where (spoiler: potema)
riften: clear a skooma operation cave, which only hapen after you cure an argonian
windhelm: either finish imperial quest line, or advance in stormcloak questline, no other ways possible

so, if you know what quest you did, you know what city you need to go to