The validity of your assumptions depend very much on your location and on the amount of energy you want to generate. Some small-scale solutions do not suffer from the same drawback as large-scale solutions.
The CO2 emitted by burning biomass is CO2 from the atmosphere that was taken up by plants and trees. This means that energy from biomass can be generated CO2-neutral, provided the biomass that is burned is replaced by the same amount of new trees and plants (and ignoring the use of non-renewable energy for transporting the biomass). There can be other drawbacks of biomass like atmospheric pollution, or edible biomass competing with food/feed and driving up prices.
However using crop residues or manure to generate methane (in a biodigester) for example and do not have these disadvantages. In this case economic viability can be a problem depending on the scale and availability of biomass.
Geothermal is indeed very efficient for providing heat and less so for providing energy, but that doesn't mean it's totally unsuitable. For example in Iceland 29% of the generated electrical energy comes from geothermal sources and 9 out of 10 households are heated with geothermal energy. Obviously in other countries with less volcanic activity geothermal energy is more costly.
I agree with you that hydro-electricity is one of the most environmental unfriendly renewable energy sources. It disrupts river flows, hinders procreation of certain types of fish, and causes methane emissions by flooding areas with vegetation. But these problems apply primarily to new to-be-built dams. Small scale hydro-electricity can solve most of these problems, and existing dams in Norway are much more environmentally friendly than dams in the tropics.
Wind and solar power
Both wind and solar power are efficient and cost-effective and have good scaling capabilities. That's also the reason these two are the fastest growing renewable energy sources. Obviously they are only suitable for regions with plenty of sunshine or wind. It's assumed that solar power is not efficient at high latitudes, but some researchers are trying to prove otherwise.
The biggest drawback of both wind and solar is that energy storage is costly and difficult, but the expectations are that the popularity of both energy sources will stimulate research for better and cheaper battery technology.
There isn't a single, renewable energy source that will solve all our problems. All renewable energy sources have their pros and cons and which type of renewable energy is best depends very much on the local circumstances and the scale you want. Often a mixture of different renewable energy sources is the best solution. In many cases solar and wind energy are the good options because they can compete with and even outperform non-renewable energy sources in terms of cost.