Gravity assists are helpful but they're not all-powerful. There's a hard constraint: your orbit is deflected more as you make your point of closest approach lower, but you can't make it too low without hitting the atmosphere. (Unless you actually want to crash into Venus instead of the sun; in which case, knock yourself out, but the moon is closer.)
Math time: a Hohmann transfer orbit from Earth to Venus will have 2.7km/sec of excess velocity when it reaches Venus. That means your orbit has a 44000km semi-major axis. With a closest approach of 6100km, that gives you a minimum eccentricity of 1.137; if I'm doing my trigonometry right, the most orbital speed you could lose in a single flyby is 4.2km/sec, or about 11% of your speed relative to the sun.
You could do better with multiple carefully-orchestrated flybys, but the point is it's not as simple as just heading for the nearest planet and letting it fling you wherever you want to go.
Math time: a Hohmann transfer orbit from Earth to Venus will have 2.7km/sec of excess velocity when it reaches Venus. That means your orbit has a 44000km semi-major axis. With a closest approach of 6100km, that gives you a minimum eccentricity of 1.137; if I'm doing my trigonometry right, the most orbital speed you could lose in a single flyby is 4.2km/sec, or about 11% of your speed relative to the sun.
(See http://en.wikipedia.org/wiki/Hohmann_transfer_orbit and http://en.wikipedia.org/wiki/Hyperbolic_trajectory for details.)
You could do better with multiple carefully-orchestrated flybys, but the point is it's not as simple as just heading for the nearest planet and letting it fling you wherever you want to go.