I'm looking for an A to B car, daily driver. I've watched a lot of Scotty's videos and I know I can trust a 4 cylinder, 4 speed Toyota Camry or Corolla.
Just want to ask if there is any specific year I should avoid due to a problem (I'm thinking between 1996 and 2010)?
Some specific ones I'm looking at are a '03 Corolla with 181k miles for $2,250, and a 01' Camry with 164k miles for $2500, would those be a good deal?
Have a look at the "I need to buy a car" topic in the FAQ. Lots of info there about which cars to avoid.
For the Camry, avoid the ones with the 2AZ-FE 2.4L 4 cylinder engine - they burn a ton of oil. Also avoid 1998-2002 Corollas because they also tended to burn a lot of oil. Between the ones you listed, I would go for the Camry because of the lower mileage and better comfort. Pay less than $2500 - it's not worth a penny over $2000. Both the cars you listed are dependable, just negotiate the price down and make sure you have the engine and transmission checked out to make sure they're still in good shape.
From what I've heard, the 2AZ-FE only had problems with oil consumption starting in 2006 for the RAV4 and 2007 for the Camry to 2009. That's when they had issues with piston rings.
Yes, you have picked two excellent cars that can last forever.
Check out the Toyota and Honda Common Problems Page linked below,
off the top of my head 1998-2002 Corolla, 2009 Corolla, 2007-2009 Camry, etc.
Those two years should be fine, have a mechanic check them out.