However, will it take another 60 years or more to reach the next planet in the solar system?
Much more, if ever. As Pearsonartphoto has pointed out: it is nearly impossible to land on any other planet. It might never happen. Even for Mars the case is very hard to make, and more governed by exploration and prestige than by science or economics.
The cost difference between staffed and unstaffed missions is very large, and the quality of robots is increasing, so the economic or scientific case for staffed missions diminishes over time.
We'll probably get humans to Mars eventually, but personally, I don't believe there will be humans on the surface Mars before 2050.
When will we land on Venus?
We will never land with humans on Venus. The surface of Venus is too hot for humans or their current technology. The surface of Venus is much harder to survive on than the Moon, Mars, or Deep Space.
How about Neptune?
We will never land with humans on Neptune.
Have any rough dates been said or is it just too far off to give a proper estimate?
Anyone who sets a date on landing on Venus or Neptune or even Ceres should do so only when writing a science fiction story and not when involved in actual space exploration.
Even for Mars, the target dates for landing keep shifting. Personally, I would be surprised if humans landed on Mars in the next 20 years. A round trip to Mars is difficult and expensive, as you have to bring (or locally build) the entire launch system to get back to Earth. A one-way trip might be more feasible, but I am skeptical if agencies are willing to invest in a one-way journey.