Alternatives to the String Landscape? Many people criticize string theory for being very speculative and far fetched (since it requires extra dimensions). Nevertheless, the string landscape is often invoked to have many variations of constants in different regions of the inflationary multiverse since ordinary GUTs only allow small variations:

"The fundamental theory of nature may admit multiple vacua with
different low-energy constants. If there were just a few vacua, as
in standard GUT models, then a few observations would determine
which one corresponds to the real world. Predictions would then follow
for every other observable in the low energy theory. However, it has
recently been realized that in the context of string theory there may
be a vast landscape of possibilities, with googols of vacua to
scan."

Alexander Vilenkin, "Probabilities in the inflationary multiverse" (2005)

"While the multiverse is rooted in the cosmological concept of eternal
inflation (Vilenkin 1983), the string landscape is necessary for
providing a physical basis for allowing different values of the
cosmological constant and other parameters in each universe of the
multiverse."

Richard Dawid, "Philosophy of String Theory" (p.9)
My question is the following: are there alternatives to the string landscape that allow for many variations of constants? Is the string landscape necessary at all to have variations in different inflationary regions?
 A: The statements here depend a bit on how loose we play with the notion of "vacuum" and how much we think we really understand about "string theory" in its non-perturbative form.
A "string theory vacuum" is just another name for a 10d manifold that we use as a target space to do perturbative string theory on (see also this question and its answers), usually by determining the effective low-energy QFT and looking at its particle spectrum if we're searching for realistic models. Since we do not have a definite formulation of non-perturbative string theory, we do not know anything about the dynamics between these "vacua", but the idea/hope/bold claim by many is that string theory should be able to somehow move between them or - just like with the false vacua in e.g. Higgs-like QFTs - have the universe be in different vacua at different places.
Since the vacuum represents the stringy target space and hence its non-compact parts the spacetime of the effective QFT, it is a bit hard to see what this statement really is supposed to mean - spacetime changes what manifold it is at different parts of spacetime? (this does not make sense, in case it is not clear) - but since we don't have any good formulation of the theory in which this can happen anyway it's moot to ask about such technical aspects.
So if you believe that there must be a full formulation of non-perturbative string theory and that the Calabi-Yau compactifications must be the vacua of this theory, then you have one physical theory that produces a gigantic variety of possible effective QFT as its vacuum states. This is often perceived as elegant because we then would have one underlying theory that produces all the others via some dynamical process, in contrast to QFT models where we have to put in the Lagrangian by hand and there is no notion of dynamics between different Lagrangians.
Without the formulation of string theory/M-theory where the dynamics between the vacua are well-defined and we actually know what the vacua are for certain, however, such statements must be viewed with a grain of salt - the people in your quotes are talking about the "grand vision" of string theory more than what it currently can do, at least to my knowledge. So in a sense it would just be an "alternative" to claim that we can have different parts of the universe use different parts of QFT without string theory and invent some other dynamics for it - the string theory version is not sufficiently nailed down as a theory on a technical level to be able to judge what really counts as an alternative.
A: 
Many people criticise string theory for being very speculative and far-fetched, since it requires extra dimensions.

It's not very well known that even electromagnetism as its incarnation as a U(1) bundle also requires extra dimensions, although here they are referred to as internal dimensions. Nevertheless, it has the same mathematical structure.
The criticism, by Smolin for example, is on the arrogance of string theorists and the lack of support for alternatives, for example, causal set theory.

Are there alternatives to the string landscape that allow for many cariation of constants?

Not as far as I know.
String theory is already speculative as is eternal inflation. Thus we are building a tower of speculations. Thus it's important to recogise that the stringy vacua also fit into a traditional landscape of quantum field theory, and by extension, to string theory.
Here, the vacuum is a non-perturbative super-position of vacua with non-perturbative instanton correction tunneling between vacua. It's a kind of condensate. Thus, the landscape can be used in an already understandable manner without branching out into yet another speculation - eternal inflation.
